Statistical Regression

In this paper we propose accurate parameter and over-identification tests for indirect inference. Under the null hypothesis the new tests are asymptotically χ 2 -distributed with a relative error of order n -1 . They exhibit better finite sample accuracy than classical tests for indirect inference, which have the same asymptotic distribution but an absolute error of order n -1/2 . Robust versions of the tests are also provided. We illustrate their accuracy in nonlinear regression, Poisson regression with overdispersion and diffusion models.

This paper introduces two practical constructs for robust one-dimensional distributional summaries: the S M Nazmuz Sakib Quantile Envelope Principle (the Sakib Principle) and the S M Nazmuz Sakib Median-of-Quartiles Theorem (the Sakib Theorem). The Sakib Principle systematizes nested central quantile envelopes E c = [Q(c), Q(1-c)] and records their invariance, coverage, and robustness. The Sakib Theorem studies the median-of-quartiles estimator M Q = 1 2 (Q(0.25) + Q(0.75)), showing its consistency for the population median under mild conditions and highlighting its stability in the presence of contamination. We situate these ideas alongside classical robust summaries (median, IQR, MAD), exploratory plots [1], and quantile theory [2, 5]. Several TikZ/pgfplots illustrations clarify the concepts, and small proofs and remarks connect with robust-statistics fundamentals [3, 4, 7, 8].

The Exponentially Weighted Moving Average (EWMA) control chart is widely implemented in applications in various fields, such as finance, medicine, engineering, and others. In real-world applications such as hospital admissions, share prices, and daily rainfall, data often exhibits both seasonal autocorrelation patterns and quadratic trend characteristics. Therefore, the application of EWMA control charts for detecting changes in processes offers significant advantages. The average run length (ARL) is commonly used as the standard criterion for measuring the efficiency of control charts. Hence, the accurate calculation of average run length with minimal processing time is an essential element of this research. This paper focuses on proposing an explicit formula for the ARL of the EWMA chart when the observations follow a seasonal autoregressive model of order P (SAR(P) L ) with quadratic trend. The proof for deriving the explicit formula of the ARL uses Fredholm's integral equation method. The application of Banach's Fixed Point Theorem provides a guarantee for solution uniqueness. Additionally, the performance of the proposed explicit formula is compared with the approximate ARL derived from Numerical Integral Equation methods, which consist of the Midpoint rule, the Trapezoidal rule, the Simpson's rule, and the Gaussian rule. The efficiency of the explicit formula of ARL is evaluated using two criteria: absolute percentage difference and the computational (CPU) time. The results obtained indicate that the ARL from the explicit formula is close to the numerical integral equation with an absolute percentage difference of less than 0.001. The proposed explicit formula has a minimal CPU time of about 0.001 seconds, while the Midpoint and Trapezoidal rules take 2 -3 seconds. The Simpson's and Gaussian rules require the longest times, approximately 9 -10 seconds. A key finding of this study was that the explicit formulas performed better than the numerical integral equation methods in terms of CPU time. As a result, both the proposed explicit formulas and the numerical integral equation methods have emerged as viable alternatives for determining the ARL of the EWMA control chart.

This paper proposes consistent estimators for transformation parameters in semiparametric models. The problem is to find the optimal transformation into the space of models with a predetermined regression structure like additive or multiplicative separability. We give results for the estimation of the transformation when the rest of the model is estimated non-or semi-parametrically and fulfills some consistency conditions. We propose two methods for the estimation of the transformation parameter: maximizing a profile likelihood function or minimizing the mean squared distance from independence. First the problem of identification of such models is discussed. We then state asymptotic results for a general class of nonparametric estimators. Finally, we give some particular examples of nonparametric estimators of transformed separable models. The small sample performance is studied in several simulations. Taking transformations of the data has been an integral part of statistical practice for many years. Transformations have been used to aid interpretability as well as to improve statistical performance. An important contribution to this methodology was made by who proposed a parametric power family of transformations that nested the logarithm and the level. They suggested that the power transformation, when applied to the dependent variable in a linear regression setting, might induce normality, error variance homogeneity and additivity of effects. They proposed estimation methods for the regression and transformation parameters. applied this and other transformations to both dependent and independent variables. A number of other dependent variable transformations have been suggested, for example, the Zellner-Revankar (1969) transform and the Bickel and Doksum (1981) transform. The transformation methodology has been quite successful and a large literature exists on this subject for parametric models; see . In survival

A common problem in applied regression analysis is that covariate values may be missing for some observations but imputed values may be available. This situation generates a trade-off between bias and precision: the complete cases are often disarmingly few, but replacing the missing observations with the imputed values to gain precision may lead to bias. In this paper we formalize this trade-off by showing that one can augment the regression model with a set of auxiliary variables so as to obtain, under weak assumptions about the imputations, the same unbiased estimator of the parameters of interest as complete-case analysis. Given this augmented model, the bias-precision trade-off may then be tackled by either model reduction procedures or model averaging methods. We illustrate our approach by considering the problem of estimating the relation between income and the body mass index (BMI) using survey data affected by item non-response, where the missing values on the main covariates are filled in by imputations.

In this paper D-and V-optimal population designs for the quadratic regression model with a random intercept term and with values of the explanatory variable taken from a set of equally spaced, non-repeated time points are considered. D-optimal population designs based on single-point individual designs were readily found but the derivation of explicit expressions for designs based on two-point individual designs was not straightforward and was complicated by the fact that the designs now depend on ratio of the variance components. Further algebraic results pertaining to d-point D-optimal population designs where dZ3 and to V-optimal population designs proved elusive. The requisite designs can be calculated by careful programming and this is illustrated by means of a simple example.

Missing covariate values is a common problem in a survival data research. The aim of this study is to compare the use of the multiple imputation (MI) and last observation carried forward (LOCF) methods for handling missing covariate values in the Cox proportional hazards (PH) regression model. The comparisons between the methods are based on simulated data. The missingness mechanism is assumed to be missing at random (MAR). Missing covariate values are generated under different missingness rates. The results from both methods are compared by assessing the bias, efficiency and coverage. The simulation results in general revealed that MI is likely to be the best under the MAR mechanism. A Simulation Study Comparing Two Methods of Handling Missing Covariate Values when Fitting a Cox ProportionalHazards Regression Model

This study aims to obtain empirical evidence of the influence of subject norms and attitudes on whistleblowing intentions. The population of this study is employees of accounting and finance department of Universitas Negeri Semarang. The research sample applied convenience sampling technique. The analysis used was PLS SEM analysis. The results of the study indicate that the attitudes and subjective norms of employees have a significant influence on whistleblowing intentions. The results of the study reinforce the theory of planned behavior that attitudes and subjective norms influence one's intention to act. This study gives a major contribution to the organization. Management of employees emotional is extremely needed to drive their attitudes and subjective norms to be a good whistleblower. For further research, it should involve a moderating variable such as organizational support to obtain more comprehensive research results.

In this paper the problem of estimating the scale matrix in a complex elliptically contoured distribution(complex ECD) is addressed. An extended Haff-Stein identity for this model is derived. It is shown that the minimax estimators of the covariance matrix obtained under the complex normal model remain robust under the complex ECD model when the Stein loss function is employed.

This paper uses model symmetries in the instrumental variable (IV) regression to derive an invariant test for the causal structural parameter. Contrary to popular belief, we show that there exist model symmetries when equation errors are heteroskedastic and autocorrelated (HAC). Our theory is consistent with existing results for the homoskedastic model and Chamberlain ( )). We use these symmetries to propose the conditional integrated likelihood (CIL) test for the causality parameter in the over-identified model. Theoretical and numerical findings show that the CIL test performs well compared to other tests in terms of power and implementation. We recommend that practitioners use the Anderson-Rubin (AR) test in the just-identified model, and the CIL test in the over-identified model.

Inferring causal relationships or related associations from observational data can be invalidated by the existence of hidden confounding. We focus on a high-dimensional linear regression setting, where the measured covariates are affected by hidden confounding and propose the Doubly Debiased Lasso estimator for individual components of the regression coefficient vector. Our advocated method simultaneously corrects both the bias due to estimation of high-dimensional parameters as well as the bias caused by the hidden confounding. We establish its asymptotic normality and also prove that it is efficient in the Gauss-Markov sense. The validity of our methodology relies on a dense confounding assumption, i.e. that every confounding variable affects many covariates. The finite sample performance is illustrated with an extensive simulation study and a genomic application. * Z. Guo and D.

Five robustifications of L 2 Boosting for linear regression with various robustness properties are considered. The first two use the Huber loss as implementing loss function for boosting and the second two use robust simple linear regression for the fitting in L 2 Boosting (i.e. robust base learners). Both concepts can be applied with or without down-weighting of leverage points. Our last method uses robust correlation estimates and appears to be most robust. Crucial advantages of all methods are that they don't compute covariance matrices of all covariates and that they don't have to identify multivariate leverage points. When there are no outliers, the robust methods are only slightly worse than L 2 Boosting. In the contaminated case though, the robust methods outperform L 2 Boosting by a large margin. Some of the robustifications are also computationally highly efficient and therefore well suited for truly high dimensional problems.

We consider post-selection inference for high-dimensional (generalized) linear models. Data carving is a promising technique to perform this task. However, it suffers from the instability of the model selector and hence may lead to poor replicability, especially in high-dimensional settings. We propose the multicarve method inspired by multisplitting, to improve upon stability and replicability. Furthermore, we extend existing concepts to group inference and illustrate the applicability of the methodology also for generalized linear models.

We study a sieve bootstrap procedure for time series with a deterministic trend. The sieve for constructing the bootstrap is based on autoregressive a p p r o ximation. Given time series data, one would rst use a preliminary estimate of the trend of the underlying time series and then approximate the noise process by a large autoregressive model of increasing order as the sample size grows. The bootstrap scheme is based on resampling estimated innovations of tted autoregressive models. We show t h e v alidity of such s i e v e bootstrap approximations for the limiting distribution of linear trend estimators, such as general regression predictors or kernel smoothers. This bootstrap scheme can then be used to construct simultaneous condence intervals for the trend, where the simultaneity c a n b e a c hieved over a range of points which can be chosen by the user. The time series context is substantially di erent from the independent set-up: methods from the independent, adapted to the dependent case, seem to loose much of their accuracy. Our resampling procedure yields satisfactory results in a simulation study for nite sample sizes.

El objetivo de esta tesis doctoral es aplicar y desarrollar tecnicas de inferencia estadistica para modelos de coeficientes variables. Por un lado, se investigan tecnicas de inferencia estadistica basadas en la verosimilitud empirica para modelos de coeficientes variables continuos y discretos, en un contexto de datos de panel con efectos fijos. Primero, demostramos que el ratio de verosimilitud empirica para el coeficiente variable es asintoticamente chi-cuadrado. El ratio es invariable a cambios de escala y no es necesaria la estimacion de la varianza. Como subproductos, proponemos los estimadores de maxima verosimilitud empirica de los coeficientes variables. Tambien obtenemos la distribucion asintotica de estos estimadores y proponemos algunos procedimientos para calcular los bandwidths empiricamente. Para demostrar la viabilidad de la tecnica y analizar sus propiedades en muestras finitas, implementamos un ejercicio de simulacion de Monte Carlo, y tambien proponemos un analisis...

We consider Bayesian inference using an extension of the family of skewelliptical distributions studied by . This new class is referred to as bimodal skew-elliptical (BSE) distributions. The elements of the BSE class can take quite different forms. In particular, they can adopt both uni-and bimodal shapes. On one hand, unimodal BSE distributions provide extended skewness and kurtosis with respect to their skew-elliptical versions. On the other hand, the bimodal case behaves similarly to mixtures of two symmetric distributions. We study the main properties of the general class and illustrate its applications to two problems involving density estimation and linear regression.

When both variables are subject to error in regression model, the least squares estimators are biased and inconsistent. The measurement error model is more appropriate to fit the data. This study focuses on the problem to construct interval estimation for fitting straight line in linear measurement error model when one of the error variances is known. We use the concepts of generalized pivotal quantity and construct the confidence interval for the slope because no pivot is available in this case. We compare the existing confidence intervals in terms of coverage probability and expected length via simulation studies. A real data example is also analyzed.

When both variables are subject to error in regression model, the least squares estimators are biased and inconsistent. The measurement error model is more appropriate to fit the data. This study focuses on the problem to construct interval estimation for fitting straight line in linear measurement error model when one of the error variances is known. We use the concepts of generalized pivotal quantity and construct the confidence interval for the slope because no pivot is available in this case. We compare the existing confidence intervals in terms of coverage probability and expected length via simulation studies. A real data example is also analyzed.

The Bayesian additive regression trees (BART) model is an ensemble method extensively and successfully used in regression tasks due to its consistently strong predictive performance and its ability to quantify uncertainty. BART combines "weak" tree models through a set of shrinkage priors, whereby each tree explains a small portion of the variability in the data. However, the lack of smoothness and the absence of an explicit covariance structure over the observations in standard BART can yield poor performance in cases where such assumptions would be necessary. The Gaussian processes Bayesian additive regression trees (GP-BART) model is an extension of BART which addresses this limitation by assuming Gaussian process (GP) priors for the predictions of each terminal node among all trees. The model's effectiveness is demonstrated through applications to simulated and real-world data, surpassing the performance of traditional modeling approaches in various scenarios.

The Bayesian additive regression trees (BART) model is an ensemble method extensively and successfully used in regression tasks due to its consistently strong predictive performance and its ability to quantify uncertainty. BART combines "weak" tree models through a set of shrinkage priors, whereby each tree explains a small portion of the variability in the data. However, the lack of smoothness and the absence of an explicit covariance structure over the observations in standard BART can yield poor performance in cases where such assumptions would be necessary. The Gaussian processes Bayesian additive regression trees (GP-BART) model is an extension of BART which addresses this limitation by assuming Gaussian process (GP) priors for the predictions of each terminal node among all trees. The model's effectiveness is demonstrated through applications to simulated and real-world data, surpassing the performance of traditional modeling approaches in various scenarios.

The Bayesian additive regression trees (BART) model is an ensemble method extensively and successfully used in regression tasks due to its consistently strong predictive performance and its ability to quantify uncertainty. BART combines "weak" tree models through a set of shrinkage priors, whereby each tree explains a small portion of the variability in the data. However, the lack of smoothness and the absence of an explicit covariance structure over the observations in standard BART can yield poor performance in cases where such assumptions would be necessary. The Gaussian processes Bayesian additive regression trees (GP-BART) model is an extension of BART which addresses this limitation by assuming Gaussian process (GP) priors for the predictions of each terminal node among all trees. The model's effectiveness is demonstrated through applications to simulated and real-world data, surpassing the performance of traditional modeling approaches in various scenarios.

The Bayesian additive regression trees (BART) model is an ensemble method extensively and successfully used in regression tasks due to its consistently strong predictive performance and its ability to quantify uncertainty. BART combines "weak" tree models through a set of shrinkage priors, whereby each tree explains a small portion of the variability in the data. However, the lack of smoothness and the absence of an explicit covariance structure over the observations in standard BART can yield poor performance in cases where such assumptions would be necessary. The Gaussian processes Bayesian additive regression trees (GP-BART) model is an extension of BART which addresses this limitation by assuming Gaussian process (GP) priors for the predictions of each terminal node among all trees. The model's effectiveness is demonstrated through applications to simulated and real-world data, surpassing the performance of traditional modeling approaches in various scenarios.

SummaryThe design of experiments for generalized non-linear models is investigated and applied to an optical process for characterizing interfaces which is widely used in the physical and natural sciences. Design strategies for overcoming the dependence of a D-optimal design on the values of the model parameters are explored, including the use of Bayesian designs. Designs for the accurate estimation of model parameters are presented and compared, as are designs for the estimation of a set of ratios of parameters which is of particular importance in the motivating example. The effectiveness of various design methods is studied, and the benefits of well-designed experiments are demonstrated.

We investigate optimal designs for discriminating between exponential regression models of different complexity, which are widely used in the biological sciences; see, e.g., Landaw (1995) or . We discuss different approaches for the construction of appropriate optimality criteria, and find sharper upper bounds on the number of support points of locally optimal discrimination designs than those given by Caratheodory's Theorem. These results greatly facilitate the numerical construction of optimal designs. Various examples of optimal designs are then presented and compared to different other designs. Moreover, to protect the experiment against misspecifications of the nonlinear model parameters, we adapt the design criteria such that the resulting designs are robust with respect to such misspecifications and, again, provide several examples, which demonstrate the advantages of our approach.

In many applications, there are multiple time series that are hierarchically organized and can be aggregated at several different levels in groups based on products, geography or some other features. We call these "hierarchical time series". They are commonly forecast using either a "bottom-up" or a "top-down" method. In this paper we propose a new approach to hierarchical forecasting which provides optimal forecasts that are better than forecasts produced by either a top-down or a bottom-up approach. Our method is based on independently forecasting all series at all levels of the hierarchy and then using a regression model to optimally combine and reconcile these forecasts. The resulting revised forecasts add up appropriately across the hierarchy, are unbiased and have minimum variance amongst all combination forecasts under some simple assumptions. We show in a simulation study that our method performs well compared to the top-down approach and the bottom-up method. It also allows us to construct prediction intervals for the resultant forecasts. Finally, we apply the method to forecasting Australian tourism demand where the data are disaggregated by purpose of visit and geographical region.

Empirical evidence suggest that many macroeconometric and financial models are subject to both instability and identification problems. We address both issues under the unified framework of time-varying information, which includes changes in instrument strength, in second moment of instruments, and in the variance of moment conditions. Our new estimation method exploits these changes for increased efficiency of the estimates of the (stable) structural parameters. We also propose a multivariate estimator for common changes in a system of linear equations. We obtain more precise estimates of the price indexation and output gap parameters than standard methods in a NKPC model.

We study the asymptotic properties of the standard GMM estimator when additional moment restrictions, weaker than the original ones, are available. We provide conditions under which these additional weaker restrictions improve the efficiency of the GMM estimator. To detect "spurious" identification that may come from invalid moments, we rely on the Hansen J-test that assesses the compatibility between existing restrictions and additional ones. Our simulations reveal that the J-test has good power properties and that its power increases with the weakness of the additional restrictions. Our theoretical characterization of the J-test provides some intuition for why that is.

Given m time series regression models, linear or not, with additive noise components, it is shown how to estimate semiparametrically the predictive probability distribution of one of the time series conditional on past random covariate data. This is done by assuming that the distributions of the residual components associated with the regression models are tilted versions of a reference distribution.

When discussing non-Gaussian spatially correlated variables, generalized linear mixed models have enough flexibility for modeling various data types. However, the maximum likelihood methods are plagued with substantial calculations for large data sets, resulting in long waiting times for estimating the model parameters. To alleviate this drawback, composite likelihood functions obtained from the product of the likelihoods of subsets of observations are used. The current paper uses the pairwise likelihood method to study the parameter estimations of spatial generalized linear mixed models. Then, we use the weighted pairwise and penalized likelihood functions to estimate the parameters of the mentioned models. The accuracy of estimates based on these likelihood functions is evaluated and compared with full likelihood function-based estimation using simulation studies. Based on our results, the penalized likelihood function improved parameter estimation. Prediction using penalized likelihood functions is applied. Ultimately, pairwise and penalized pairwise likelihood methods are applied to analyze count real data sets.

It is more and more frequently the case in applications that the data we observe come from one or more random variables taking values in an infinite dimensional space, e.g. curves. The need to have tools adapted to the nature of these data explains the growing interest in the field of functional data analysis. The model we study in this paper assumes a linear dependence between a quantity of interest and several covariates, at least one of which has an infinite dimension. To select the relevant covariates in this context, we investigate adaptations of the Lasso method. Two estimation methods are defined. The first one consists in the minimization of a Group-Lasso criterion on the multivariate functional space H. The second one minimizes the same criterion but on a finite dimensional subspaces of H whose dimension is chosen by a penalized least squares method. We prove oracle inequalities of sparsity in the case where the design is fixed or random. To compute the solutions of both criteria in practice, we propose a coordinate descent algorithm. A numerical study on simulated and real data illustrates the behavior of the estimators.

We propose a new regression method to estimate the impact of explanatory variables on quantiles of the unconditional (marginal) distribution of an outcome variable. The proposed method consists of running a regression of the (recentered) influence function (RIF) of the unconditional quantile on the explanatory variables. The influence function is a widely used tool in robust estimation that can easily be computed for each quantile of interest. We show how standard partial effects, as well as policy effects, can be estimated using our regression approach. We propose three different regression estimators based on a standard OLS regression (RIF-OLS), a logit regression (RIF-Logit), and a nonparametric logit regression (RIF-OLS). We also discuss how our approach can be generalized to other distributional statistics besides quantiles.

In this paper, we attempt to address the robustness issues in circular-circular regression. We consider the Möbius transformation based circular-circular regression model of Kato et al. (2008). Then, we discuss the robustness issue of the estimators in this model. We propose maximum trimmed cosine estimator in this context and discuss the algorithm for its computation. We also discuss some properties including the breakdown point of the estimators. Simulation studies and a real data analysis are used to illustrate the proposed methodology.

We consider a continuous-time stochastic volatility model. The model contains a stationary volatility process, the multivariate density of the finite dimensional distributions of which we aim to estimate. We assume that we observe the process at discrete instants in time. The sampling times will be equidistant with vanishing distance. A multivariate Fourier-type deconvolution kernel density estimator based on the logarithm of the squared processes is proposed to estimate the multivariate volatility density. An expansion of the bias and a bound on the variance are derived.

The Cube method proposed by enables the selection of balanced samples : that is, samples such that the Horvitz-Thompson estimators of auxiliary variables match the known totals of those variables. As an exact balanced sampling design often does not exist, the Cube method generally proceeds in two steps : a "flight phase" in which exact balance is maintained, and a "landing phase" in which the final sample is selected while respecting the balance conditions as closely as possible. Deville and Tillé (2005) derive a variance approximation for balanced sampling that takes account of the flight phase only, whereas the landing phase can prove to add non-negligible variance. This paper uses a martingale difference representation of the cube method to construct an efficient simulationbased method for calculating approximate second-order inclusion probabilities. The approximation enables nearly unbiased variance estimation, where the bias is primarily due to the limited number of simulations. In a Monte Carlo study, the proposed method has significantly less bias than the standard variance estimator, leading to improved confidence interval coverage.

Maximum likelihood estimation is investigated in the context of linear regression models under partial independence restrictions. These restrictions aim to assume a kind of completeness of a set of predictors Z in the sense that they are sufficient to explain the dependencies between an outcome Y and predictors X: L(Y|Z, X) ¼ L(Y|Z), where L(AE|AE) stands for the conditional distribution. From a practical point of view, the former model is particularly interesting in a double sampling scheme where Y and Z are measured together on a first sample and Z and X on a second separate sample. In that case, estimation procedures are close to those developed in the study of double-regression by Causeur &. Properties of the estimators are derived in a small sample framework and in an asymptotic one, and the procedure is illustrated by an example from the food industry context.

A basic assumption concerned with general linear regression model is that there is no correlation (or no multicollinearity) between the explanatory variables. When this assumption is not satisfied, the least squares estimators have large variances and become unstable and may have a wrong sign. Therefore, we resort to biased regression methods, which stabilize the parameter estimates. Ridge regression (RR) and principal components regression (PCR) are two of the most popular biased regression methods. In this article, we used Monte Carlo experiments to estimate the regression coefficients by RR and PCR methods. A comparison between RR and PCR methods was made in the sense of having smaller mean squares error (MSE). Based on this simulation study, we found that RR method performs better than PCR method.

fitting. Their sampling properties such as bias and variance and asymptotic distributions can be derived. Estimators of their biases and variances can easily be formulated. The global modeling and the local modeling approach both have strengths in their own domain of applications. Together they provide invaluable tools for nonlinear data analyses and foundational insights.

In this research, a comparison was made between two methods for estimating a semiparametric regression model with the presence of an autocorrelation problem, based on a semiparametric partial linear regression model, which contains a parametric component and a nonparametric component. The two components were estimated using two methods, the first methods is semi parametric generalized least squares estimators(SGLSE) , the second methods is least squares estimators method(LSEM) .Simulation study show the first method is beast than the second method by using mean squares of errors (MSE) .

In this paper we propose a new framework for Bayesian nonparametric modelling with continuous covariates. In particular, we allow the nonparametric distribution to depend on covariates through ordering the random variables building the weights in the stick-breaking representation. We focus mostly on the class of random distributions which induces a Dirichlet process at each covariate value. We derive the correlation between distributions at different covariate values, and use a point process to implement a practically useful type of ordering. Two main constructions with analytically known correlation structures are proposed. Practical and efficient computational methods are introduced. We apply our framework, though mixtures of these processes, to regression modelling, the modelling of stochastic volatility in time series data and spatial geostatistical modelling.

The vast majority of work done on inventory system is based on the critical assumption of fully observed inventory inventory level dynamics and demand. Modern technology, like the internet, offers a tremendous number of opportunities to businesses to collect imperfect but useful information which helps them planning efficiently to meet future demand. A good example is the internet. Visits to commercial web sites constitute a source of partial information on future demands of one or more of the commodities (or services) offered by companies. Many factors contribute to make inventories hard to be fully observed by the management. Using Hidden Markov Models techniques we exploit partial information on inventory systems to estimate the current inventory level as well as future demands. The parameters of the model are updated via the EM algorithm.

This state-level analysis of 2022 vehicle death rates across all 50 states (and the District of Columbia) finds that income inequality and educational attainment are key factors, with contributions also from seat belt use, urbanicity, and obesity

Semi-parametric Gaussian mixtures of non-parametric regressions (SPGMNRs) are a flexible extension of Gaussian mixtures of linear regressions (GMLRs). The model assumes that the component regression functions (CRFs) are non-parametric functions of the covariate(s) whereas the component mixing proportions and variances are constants. Unfortunately, the model cannot be reliably estimated using traditional methods. A local-likelihood approach for estimating the CRFs requires that we maximize a set of local-likelihood functions. Using the Expectation-Maximization (EM) algorithm to separately maximize each local-likelihood function may lead to label-switching. This is because the posterior probabilities calculated at the local E-step are not guaranteed to be aligned. The consequence of this label-switching is wiggly and non-smooth estimates of the CRFs. In this paper, we propose a unified approach to address label-switching and obtain sensible estimates. The proposed approach has two stages. In the first stage, we propose a model-based approach to address the label-switching problem. We first note that each local-likelihood function is a likelihood function of a Gaussian mixture model (GMM). Next, we reformulate the SPGMNRs model as a mixture of these GMMs. Lastly, using a modified version of the Expectation Conditional Maximization (ECM) algorithm, we estimate the mixture of GMMs. In addition, using the mixing weights of the local GMMs, we can automatically choose the local points where local-likelihood estimation takes place. In the second stage, we propose one-step backfitting estimates of the parametric and non-parametric terms. The effectiveness of the proposed approach is demonstrated on simulated data and real data analysis.

The paper studies GMM inference for subvector hypotheses in structural models where nuisance parameters may not be identified. Such testing problems are often assessed using the plug-in principle (Stock and Wright, 2000) or the projection method (Dufour and Taamouti, 2005), but it is now well documented that both methods have substantial drawbacks when the nuisance structural parameters are weakly identified. We show that for the class of linear GMM models, there exists a mapping that leaves the subset null hypothesis of interest invariant and eliminates the non-identified components of the nuisance parameters, while preserving those that are identified. Therefore, identification-robust inference can be drawn uniformly for the subset testing problem of interest using the conventional plug-in method once the mapping is applied. We exploit this result to develop the score, Lagrange multiplier, and conditional likelihood ratio type-tests for the subset null hypothesis considered. In ad...

We develop inference and testing procedures for conditional dispersion and skewness in a nonparametric regression setup based on statistical depth functions. The methods developed can be applied in situations, where the response is multivariate and the covariate is a random element in a metric space. This includes regression with functional covariate as a special case. We construct measures of the center, the spread and the skewness of the conditional distribution of the response given the covariate using depth based nonparametric regression procedures. We establish the asymptotic consistency of those measures and develop a test for heteroscedasticity and a test for conditional skewness. We present level and power study for the tests in several simulated models. The usefulness of the methodology is also demonstrated in a real dataset. In that dataset, our responses are the nutritional contents of different meat samples measured by their protein, fat and moisture contents, and the fu...

Quantitative hydrologic forecasting usually requires knowledge of the spatial and temporal distribution of precipitation. First, it is important to accurately measure the precipitation falling over a particular watershed of interest. Second, especially for small watersheds and/or for longer forecast lead times, forecasts of precipitation are critical to the achievement of the greatest possible hydrologic forecast accuracy and longest possible lead time. This paper describes the current hydrologic forecasting program of the U.S. National Weather Service (NWS) and highlights the relevance of Quantitative Precipitation Forecasting (QPF) products to real-time hydrologic forecasting. Specific requirements for QPF products in support of hydrologic forecasting applications are defined and current operational QPF procedures are reviewed to determine to what extent they meet these requirements. It is concluded that no known QPF procedures capable of fulfilling all desired requirements are currently available operationally, although much valuable QPF information is available to meet parts of these requirements. Some recent advances in mesoscale QPF research are examined and these techniques are treated in two categories: those uncoupled dynamically from and those dynamically coupled to hydrologic forecasting procedures. Finally, a summary of possible future directions toward achieving improved use of QPF information in hydrologic forecasting applications is presented.