Randomly censored partially linear single-index models

This paper proposes a method for estimation of a class of partially linear single-index models with randomly censored samples. The method provides a flexible way for modelling the association between a response and a set of predictor variables when the response variable is randomly censored. It pres...

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Vydáno v:	Journal of multivariate analysis Ročník 98; číslo 10; s. 1895 - 1922
Hlavní autoři:	Lu, Xuewen, Cheng, Tsung-Lin
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	San Diego, CA Elsevier Inc 01.11.2007 Elsevier Taylor & Francis LLC
Edice:	Journal of Multivariate Analysis
Témata:	Accelerated failure-time model Accelerated failure-time model Asymptotic normality Kernel smoothing Local linear fit Partially linear single-index model Quasi likelihood Random censoring Synthetic data Asymptotic normality Distribution theory Estimating techniques Exact sciences and technology Kernel smoothing Linear inference, regression Local linear fit Mathematical models Mathematics Monte Carlo simulation Multivariate analysis Nonparametric inference Partially linear single-index model Probability and statistics Quasi likelihood Random censoring Random variables Regression analysis Sciences and techniques of general use Statistics Studies Survival analysis Synthetic data 62N01 62G08 Asymptotic normality Quasi likelihood 62E20 Kernel smoothing Partially linear single-index model Random censoring Accelerated failure-time model Local linear fit Synthetic data Statistical distribution Censored sample Non parametric estimation Multivariate analysis Kernel estimator Stochastic method Asymptotic convergence Linear model Semiparametric model Survival function Failure analysis Regression function Approximation theory Survival model 62N01; 62G08; 62E20 Censored data Monte Carlo method Linear regression Statistical association Statistical estimation Semiparametric method Algorithm Survival iccelerated failure-time model; Asymptotic normality; Kernel smoothing; Local linear fit; Partially linear single-index model; Quasi likelihood; Random censoring; Synthetic data Kernel method Statistical method Kernels Statistical regression Survival analysis Regression coefficient Kernel function Dimension reduction Numerical analysis Simulation Regression model Survival time Failure time
ISSN:	0047-259X, 1095-7243
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Popis
Shrnutí:	This paper proposes a method for estimation of a class of partially linear single-index models with randomly censored samples. The method provides a flexible way for modelling the association between a response and a set of predictor variables when the response variable is randomly censored. It presents a technique for “dimension reduction” in semiparametric censored regression models and generalizes the existing accelerated failure-time models for survival analysis. The estimation procedure involves three stages: first, transform the censored data into synthetic data or pseudo-responses unbiasedly; second, obtain quasi-likelihood estimates of the regression coefficients in both linear and single-index components by an iteratively algorithm; finally, estimate the unknown nonparametric regression function using techniques for univariate censored nonparametric regression. The estimators for the regression coefficients are shown to be jointly root- n consistent and asymptotically normal. In addition, the estimator for the unknown regression function is a local linear kernel regression estimator and can be estimated with the same efficiency as all the parameters are known. Monte Carlo simulations are conducted to illustrate the proposed methodology.
Bibliografie:	SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14
ISSN:	0047-259X 1095-7243
DOI:	10.1016/j.jmva.2006.11.008