Hazard regression with noncompactly supported bases

Biometrika, 1992

Left truncation and right censoring arise frequently in practice for life data. This paper is concerned with the estimation of the hazard rate function for such data. Two types of nonparametric estimators based on kernel smoothing methods are considered. The first one is obtained by convolving a kernel with a cumulative hazard estimator. The second one is in the form of a ratio of two statistics. Local properties including consistency, asymptotic normality and mean squared error expressions are presented for both estimators. These properties facilitate locally adaptive bandwidth choice. The two types of estimators are then compared based on their theoretical and empirical performances. The effect of overlooking the truncation factor is demonstrated through the Channing House data.

Periodica Mathematica Hungarica, 1981

In reliability and survival-time studies one frequently encounters the following random censorship model: X1, Y~, X~, Y~ .... is an independent sequence of nonnegative rv's, the X,'s having common distribution F and the Yn's having common distribution G, Z n-~ rain {Xn, Yn}, Tn-~ I[x~Kvn]; if X n represents the (potential) time to death of the n-th individual in the sample and Yn is his (potential) censoring time then Zn represents the actual observation time and T n represents the type of observation (T n ~ 0 is a censoring, T n ~-1 is a death). One way to estimate F from the observations Z1. T1, g2, Te,. .. (and without recourse to the Xa's) is ~ means of the producg l~nit estimator Fn (K~Ae~_W and MEIER [6]). It is shown that I Fg

Annals of the Institute of Statistical Mathematics, 1993

Nonparametric kernel estimators for hazard functions and their derivatives are considered under the random left truncation model. The estimator is of the form of sum of identically distributed but dependent random variables. Exact and asymptotic expressions for the biases and variances of the estimators are derived. Mean square consistency and local asymptotic normality of the estimators are established. Adaptive local bandwidths are obtained by estimating the optimal bandwidths consistently.

2016

The purpose of this study is to estimate the right-censored nonparametric model with kernel smoothing method. To consider the censorship, we used Kaplan-Meier estimator proposed by Stute (1993). In nonparametric statistics, a kernel smoothing method needs a smoothing parameter which is also called as a bandwidth parameter. In this study, we choose the bandwidth parameter by using three selection methods such as improved version of Akaike information criterion (AICc), Risk estimation using classical pilots (RECP) and Generalized cross-validation(GCV) method, respectively. For this purpose, a Monte-Carlo simulation study is performed to illustrate which selection criterion gives the best estimation for different sample sizes and censoring levels. Key-Words: Kernel Smoothing, Kaplan-Meier Estimator, Nonparametric Regression, Censored data

Communications in Statistics - Theory and Methods, 2008

This paper studies hazard rate estimation for right-censored data by projection estimator methods. We consider projection spaces generated by trigonometric or piecewise polynomials, splines or wavelet bases. We prove that the estimator reaches the standard optimal rate associated with the regularity of the hazard function, provided that the dimension of the projection space is relevantly chosen. Then we provide an adaptive procedure leading to an automatic choice of this dimension via a penalized minimum contrast estimator and automatically reaching the optimal rate. Our procedure is based on a random penalty function and is completely data driven. A small simulation experiment is provided, that compares our result with some others.

Journal of Econometrics, 1986

This paper introduces a semi-parametric method for estimating regression coefficients when the underlying parent population of errors in censored. The method is an example of the method of sieves: and it provides simultaneous estimates of the regression coefficients and the density of the underlying parent population. In the very simplest terms, the underlying unknown density is approximated by a spline with mesh size approaching zero with the sample size. The values of the density at the knots are then added to the list of the usual unknown parameters in a censored regression model, e.g., the regression coefficients and scale parameter. A quasi-likelihood function using the approximate spline density is then maximized over all the parameters mentioned above. The method is shown to result in strongly consistent parameter estimates. *I am indebted to O= {(0,,,f3T)lO1(&1b, &EB, BcRP, Bcompact}, _cd= a(t)la(t)~C' [-l,l],/ila(l)df=I, ( J ' a(t)df= 4, cu(t) 2 0 .

Statistical Modelling, 2017

In this article, we consider an additive hazards semiparametric model for left-truncated and right-censored data where the risk function has a partly linear structure, we call it the partly linear additive hazards model. The nonlinear components are assumed to be B-splines functions, so the model can be viewed as a semiparametric model with an unknown baseline hazard function and a partly linear parametric risk function, which can model both linear and nonlinear covariate effects, hence is more flexible than a purely linear or nonlinear model. We construct a pseudo-score function to estimate the coefficients of the linear covariates and the B-spline basis functions. The proposed estimators are asymptotically normal under the assumption that the true nonlinear functions are B-spline functions whose knot locations and number of knots are held fixed. On the other hand, when the risk functions are unknown non-parametric functions, the proposed method provides a practical solution to the...

Advances and Applications in Statistics, 2022

Censoring of the dependent variable is a very common problem with micro data where under certain conditions, only the observable values of the dependent variables are the ones being recorded and not the true data points. Thus, ignoring censoring will generally lead to inconsistent estimators [2, 9]. As a result, the standard ordinary least squares regressions can come up with bias and inconsistent estimates [7-9]. In handling censored data, the commonly used estimators in the literatures were Tobit and CLAD. However, they were only tested for interval-censored data [8]. This paper extends the work to left￾censored data and presents the finite sample performances of these estimators for left-censored regression model including the new estimator which is based from a new imputation approach. Simulation results showed that as in the case of normal errors in the univariate regression case, the Tobit, CLAD, and the new estimator were consistent estimators for left censored regression model. It is also showed that Tobit is superior among the others when the errors are normal. Results also showed that the CLAD estimator is consistent for normal errors. Meanwhile, the new imputation approach produced a consistent estimator for normal errors. Although, it did not out performed Tobit and CLAD, it showed a favourable results in terms of its variance as n gets higher.

2008

This paper focuses on the problem of the estimation of the cumulative hazard function of a distribution on a general complete separable metric space when the data points are subject to censoring by an arbitrary adapted random set. A problem involving observability of the estimator proposed in [8] and [9] is resolved and a functional central limit theorem is proven for the revised estimator. Several examples and applications are discussed, and the validity of bootstrap methods is established in each case.

SSRN Electronic Journal, 1997

for writen comments and Barbara Harrow for editing assitance. We thank Duke University and the Foundation Francisco Marroquín for financial support. An electronic version of the paper can be obtained in postscript format as "pub/man/papers/npecross.ps" on lewis.econ.duke.edu.