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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Bibliographic Details
Published in:Journal of multivariate analysis Vol. 98; no. 10; pp. 1895 - 1922
Main Authors: Lu, Xuewen, Cheng, Tsung-Lin
Format: Journal Article
Language:English
Published: San Diego, CA Elsevier Inc 01.11.2007
Elsevier
Taylor & Francis LLC
Series:Journal of Multivariate Analysis
Subjects:
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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Summary: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.
Bibliography:SourceType-Scholarly Journals-1
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ISSN:0047-259X
1095-7243
DOI:10.1016/j.jmva.2006.11.008