Papers by Dr. Shalini Chandra
In the case of ill-conditioned design matrix in linear regression model, the r-(k,d) class estima... more In the case of ill-conditioned design matrix in linear regression model, the r-(k,d) class estimator was proposed and this includes, among others, the ordinary least squares (OLS) estimator, the principal component regression (PCR) estimator and the two-parameter class estimator. In this paper, the performance of the r-(k,d) class estimator over the others has been evaluated under the weighted quadratic loss function where the weights are inverse of the variance-covariance matrix of the estimator, which is also known as the Mahalanobis loss function using the criterion of average loss. Tests verifying the conditions for superiority of the r-(k,d) class estimator over the others have also been proposed. Finally, a simulation study and also an empirical illustration have been done to study the performance of the tests and hence verify the conditions of dominance of the r-(k,d) class estimator over the others under the Mahalanobis loss function in articially generated data sets and als...
In the case of ill-conditioned design matrix in linear regression model, the r-(k,d) class estima... more In the case of ill-conditioned design matrix in linear regression model, the r-(k,d) class estimator was proposed and this includes, among others, the ordinary least squares (OLS) estimator, the principal component regression (PCR) estimator and the two-parameter class estimator. In this paper, the performance of the r-(k,d) class estimator over the others has been evaluated under the weighted quadratic loss function where the weights are inverse of the variance-covariance matrix of the estimator, which is also known as the Mahalanobis loss function using the criterion of average loss. Tests verifying the conditions for superiority of the r-(k,d) class estimator over the others have also been proposed. Finally, a simulation study and also an empirical illustration have been done to study the performance of the tests and hence verify the conditions of dominance of the r-(k,d) class estimator over the others under the Mahalanobis loss function in artificially generated data sets and also for a real data set.
International Journal of Scientific & Technology Research, 2015
This paper develops an economic production quantity inventory model for deteriorating items; the ... more This paper develops an economic production quantity inventory model for deteriorating items; the rate of deterioration is Weibull distribution deterioration with two parameters. The rate of demand is stock dependent. Shortages are not allowed. The aim of this study is to find the optimal solution for minimizing the total inventory costs. To optimize the model a numerical illustration has been carried out and a sensitivity analysis occurred to study the result of parameters on assessment variables and the entire cost of this model.
In econometric research, misspecification due to omission of relevant variables is a very common ... more In econometric research, misspecification due to omission of relevant variables is a very common phenomena, which leads to biased and inconsistent estimation of parameters. It is needless to mention that the explanatory variables in the misspecified model may be multicollinear and have adverse effects on the least squares estimator. To combat the problem of multicollinearity, several biased estimators have been introduced and widely analyzed under mean squared error criterion when there is no misspecification. Furthermore, Mahalanobis loss function, which is a weighted quadratic loss function has gained quite an attention as a comparison criterion in recent years. Although, not much literature is available on the comparison of the estimators in the presence of multicollinearity under the Mahalanobis loss function when there is no misspecification and is almost negligible in case of misspecification due to omission of relevant variables. This article evaluates the performance of some...
Biostatistics and Biometrics Open Access Journal, Jun 27, 2017
Women's health has always been a topic of concern in underdeveloped and developing countries. Bas... more Women's health has always been a topic of concern in underdeveloped and developing countries. Based on the trends and estimates obtained from National Family Health Surveys in India using statistical tools, the government has taken numerous steps towards improving the health conditions of women across all states of the country. One such important statistical tool which is being widely used these days is survival analysis. In this article, we have reviewed the applications of the techniques of survival analysis in determining the factors associated with women's health in India.
Far East Journal of Mathematical Sciences (FJMS), 2018
In 2003, Liu [16] proposed a new estimator dealing with the problem of multicollinearity in linea... more In 2003, Liu [16] proposed a new estimator dealing with the problem of multicollinearity in linear regression model pointing out a drawback of ridge estimator used in this context. This new estimator, called Liu-type estimator was demonstrated to have lesser mean squared error than ridge estimator and ordinary least squares estimator, however, it may carry a large amount of bias. In the present paper, we propose different estimators in order to reduce the bias of Liu-type estimator, one using the Jackknife technique and other using the technique proposed in Kadiyala [11]. We also investigate the Bootstrap method of bias correction on the Liu-type estimator as well. The bias and mean squared error of these estimators have been compared using a simulation study as well as a numerical example.
New Trends in Mathematical Science, 2018
In multiple regression analysis, the use of ridge regression estimator over the conventional ordi... more In multiple regression analysis, the use of ridge regression estimator over the conventional ordinary least squares estimator was suggested by Hoerl and Kennard in 1970 to beat the problem of multicollinearity that may exist among the independent variables. Keeping this in mind, in the present study, the authors intend to develop and compare different confidence intervals for regression coefficients based on ridge regression estimator using bootstrap and jackknife methodology. For comparison, the coverage probabilities and confidence widths are calculated through a simulation study for the data which suffers from the problem of multicollinearity.
International Journal of Mathematics and Mathematical Sciences, 2017
It is a well-established fact in regression analysis that multicollinearity and autocorrelated er... more It is a well-established fact in regression analysis that multicollinearity and autocorrelated errors have adverse effects on the properties of the least squares estimator. Huang and Yang (2015) and Chandra and Tyagi (2016) studied the PCTP estimator and the r-(k,d) class estimator, respectively, to deal with both problems simultaneously and compared their performances with the estimators obtained as their special cases. However, to the best of our knowledge, the performance of both estimators has not been compared so far. Hence, this paper is intended to compare the performance of these two estimators under mean squared error (MSE) matrix criterion. Further, a simulation study is conducted to evaluate superiority of the r-(k,d) class estimator over the PCTP estimator by means of percentage relative efficiency. Furthermore, two numerical examples have been given to illustrate the performance of the estimators.
Uncertain Supply Chain Management, 2015
In this paper, an integrated production-inventory model with multi-item is developed from the per... more In this paper, an integrated production-inventory model with multi-item is developed from the perspectives of single producer, multiple suppliers and retailers. In this three-layer supply chain, the retailers are non-competing. Every supplier delivers only single type of raw material to the producer. The producer manufactures finished goods from the combination of fixed percentage of different types of raw materials. The producer manufactures various types of objects and supplies them to retailers according to the demand of multiple retailers. This paper studies the impact of different types of business policies such as exponential demand rate, demand dependent production rate, optimum order size of raw materials, and unit production cost at each stage of integrated marketing system. Mathematica is used to develop the model and to optimize the integrated profit function. A numerical example and sensitivity analysis is illustrated to justify the feasibility of the proposed model.
A two-warehouse inventory model for deteriorating items under conditionally permissible delay in payment
Applied Mathematical Modelling, 2011
For the capacity of any warehouse is limited, it has to rent warehouse (RW) for storing the exces... more For the capacity of any warehouse is limited, it has to rent warehouse (RW) for storing the excess units over the fixed capacity W of the own warehouse (OW) in practice. The RW is assumed to offer better preserving facilities than the OW resulting in a lower rate of deterioration and is assumed to charge higher holding cost than the OW. In this paper, a two-warehouse inventory model for deteriorating items is considered with constant demand under conditionally permissible delay in payment. The purpose of this study is to find the optimal replenishment policies for minimizing the total relevant inventory costs. Useful theorems to characterize the optimal solutions have been derived. Furthermore, numerical examples are provided to illustrate the proposed model, sensitivity analysis of the optimal solutions with respect to major parameters is carried out and some managerial inferences are obtained.
Communications in Statistics - Theory and Methods, 2014
Singh et al. (1986) proposed an almost unbiased ridge estimator using Jackknife method that requi... more Singh et al. (1986) proposed an almost unbiased ridge estimator using Jackknife method that required transformation of the regression parameters. This article shows that the same method can be used to derive the Jackknifed ridge estimator of the original (untransformed) parameter without transformation. This method also leads in deriving easily the second order Jackknifed ridge that may reduce the bias further. We further investigate the performance of these estimators along with a recent method by Batah et al. (2008) called modified Jackknifed ridge theoretically as well as numerically.
Statistics in Transition New Series, 2017
In this paper, the effect of misspecification due to omission of relevant variables on the domina... more In this paper, the effect of misspecification due to omission of relevant variables on the dominance of the r -(k,d) class estimator proposed by Özkale (2012), over the ordinary least squares (OLS) estimator and some other competing estimators when some of the regressors in the linear regression model are correlated, have been studied with respect to the mean squared error criterion. A simulation study and numerical example have been demostrated to compare the performance of the estimators for some selected values of the parameters involved.
In this study, Naive I & Naive II, Grey and vector error correction (VEC) models are applied to f... more In this study, Naive I & Naive II, Grey and vector error correction (VEC) models are applied to forecast foreign tourist arrivals (FTAs) to India. Bates and Granger (1969) developed combination of forecasts by using the various combination methods in order to improve the single forecasts accuracy. Therefore, the combination methods based on simple average (SA) and inverse of mean absolute percentage error (IMAPE) is applied to improve the efficiency of individual forecasting methods. The data of FTAs to India from January 2003 to December 2016 obtained from http://www.indiastat.com are used for the overall empirical analysis. The results of the empirical study show that the combination forecasts have a better accuracy than the individual forecasts under root mean square error (RMSE), mean absolute percentage error (MAPE) and U-statistic (U) criteria. The study also demonstrates that the inverse of MAPE combination method is more suitable for forecasting of FTAs than simple average a...
International Journal of Computing Science and Mathematics
This study aims to compare various time series models to forecast monthly foreign tourist arrival... more This study aims to compare various time series models to forecast monthly foreign tourist arrivals to India. The models which are considered here include Naive I & Naive II, seasonal autoregressive integrated moving average (SARIMA) and Grey models. The forecasting performance of these models has been compared under mean absolute percentage error (MAPE), U-statistic and turning point analysis (TPA) criteria. Empirical findings show that Naive I gives better forecast of foreign tourist arrivals to India relative to other time series models under MAPE and U-statistic criteria. In addition, SARIMA is found to be better model as compared to other models according to TPA criterion.
Journal of data science, 2021
This study aims to compare various quantitative models to forecast monthly foreign tourist arriva... more This study aims to compare various quantitative models to forecast monthly foreign tourist arrivals (FTAs) to India. The models which are considered here include vector error correction (VEC) model, Naive I and Naive II models, seasonal autoregressive integrated moving average (SARIMA) model and Grey models. A model based on combination of single forecast values using simple average (SA) method has also been applied. The forecasting performance of these models have been compared under mean absolute percentage error (MAPE) and U-statistic (Ustat) criteria. Empirical findings suggest that the combination model gives better forecast of FTAs to India relative to other individual time series models considered here.
International Econometric Review, 2015
In the case of ill-conditioned design matrix in linear regression model, the r-(k, d) class estim... more In the case of ill-conditioned design matrix in linear regression model, the r-(k, d) class estimator was proposed, including the ordinary least squares (OLS) estimator, the principal component regression (PCR) estimator, and the two-parameter class estimator. In this paper, we opted to evaluate the performance of the r-(k, d) class estimator in comparison to others under the weighted quadratic loss function where the weights are inverse of the variance-covariance matrix of the estimator, also known as the Mahalanobis loss function using the criterion of average loss. Tests verifying the conditions for superiority of the r-(k, d) class estimator have also been proposed. Finally, a simulation study and also an empirical illustration have been done to study the performance of the tests and hence verify the conditions of dominance of the r-(k, d) class estimator over the others under the Mahalanobis loss function in artificially generated data sets and as well as for a real data. To the best of our knowledge, this study provides stronger evidence of superiority of the r-(k, d) class estimator over the other competing estimators through tests for verifying the conditions of dominance, available in literature on multicollinearity.
Statistical Papers, 2015
In this paper, a new estimator called the restricted r-k class estimator, is introduced when the ... more In this paper, a new estimator called the restricted r-k class estimator, is introduced when the linear restrictions binding the regression coefficients are stochastic in nature, by combining the ordinary ridge regression estimator and principal component regression estimator for a regression model suffering from the problem of multicollinearity. The performance of the proposed r-k class estimator in the mixed regression model is compared with that of the mixed regression estimator and the stochastic ridge regression estimator in terms of the mean square error matrix criterion. Tests for verifying the conditions of dominance of the proposed estimator over the two others are also proposed. Furthermore, a Monte Carlo study and a numerical evaluation are carried out to study the performance of the tests involving conditions of superiority of the proposed estimator over the other two.
Brazilian Journal of Probability and Statistics
The presence of multicollinearity adversely affects the inferential properties of the maximum lik... more The presence of multicollinearity adversely affects the inferential properties of the maximum likelihood (ML) estimator in logistic regression model. It is a well established fact that the use of restrictions lowers the effect of multicollinearity. In this article, an alternative to the ML estimator has been introduced by combining the exact prior information into the logistic r − k class (Lrk) estimator. The estimator is named a logistic restricted r − k class estimator. Another estimator, logistic restricted PCR estimator, is also developed as a special case of the LRrk estimator. The asymptotic mean squared error (MSE) matrix properties of the estimators are studied and necessary and sufficient conditions are derived. Further, a Monte Carlo simulation study is performed to compare the performance of the estimators in terms of the scalar MSE and the prediction MSE. It is found that the proposed estimators perform better than the existing estimators in most of the cases considered. Moreover, a numerical example has also been presented for comparing the performance of the estimators.
International Journal of Industrial Engineering Computations, 2014
The objective of this paper is to develop an integrated production inventory model for reworkable... more The objective of this paper is to develop an integrated production inventory model for reworkable items with exponential demand rate. This is a three-layer supply chain model with perspectives of supplier, producer and retailer. Supplier delivers raw material to the producer and finished goods to the retailer. We consider perfect and imperfect quality products, product reliability and reworking of imperfect items. After screening, defective items reworked at a cost just after the regular manufacturing schedule. At the beginning, the manufacturing system starts produce perfect items, after some time the manufacturing system can undergo into "out-of-control" situation from "in-control" situation, which is controlled by reverse logistic technique. This paper deliberates the effects of business strategies like optimum order size of raw material, exponential demand rate, production rate is demand dependent, idle times and reverse logistics for an integrated marketing system. Mathematica is used to develop the optimal solution of production rate and raw material order for maximum expected average profit. A numerical example and sensitivity analysis is illustrated to validate the model.
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Papers by Dr. Shalini Chandra