Empirical Likelihood for Generalized Functional-Coefficient Regression Models with Multiple Smoothing Variables under Right Censoring Data

Hong-Xia Xu,Guo-Liang Fan,Han-Sheng Zhong

doi:10.1155/2020/1261426

Hong-Xia Xu, Guo-Liang Fan + Show 1 more

Open Access

https://doi.org/10.1155/2020/1261426

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Abstract

Empirical likelihood as a nonparametric approach has been demonstrated to have many desirable merits for constructing a confidence region. The purpose of this article is to apply the empirical likelihood method to study the generalized functional-coefficient regression models with multiple smoothing variables when the response is subject to random right censoring. The coefficient functions with multiple smoothing variables can accommodate various nonlinear interaction effects between covariates. The empirical log-likelihood ratio of an unknown parameter is constructed and shown to have a standard chi-squared limiting distribution at the true parameter. Based on this, the confidence region of the unknown parameter can be constructed. Simulation studies are carried out to indicate that the empirical likelihood method performs better than a normal approximation-based approach for constructing the confidence region.

Highlights

In studying the relationship between a response and a set of predictor variables or regressors, the mean response variable is often assumed to be a linear regression function of the regressors
There has been increasing interest and activity in the general area of semiparametric regression modeling in statistics to analyse the high-dimensional data
Semiparametric models are often employed in regression analysis because they well balance between flexibility and fidelity

Summary

Introduction

In studying the relationship between a response and a set of predictor variables or regressors, the mean response variable is often assumed to be a linear regression function of the regressors. E semiparametric functional-coefficient regression models with multiple smoothing variables have the following form:. When the response was random right censored, Buckley and James [14] gave a method of estimating parameters in the linear regression model; Bravo [15] considered the problem of estimation and inference in semiparametric varying-coefficients partially linear models; for semiparametric varying-coefficient models with different smoothing variables, Yang [16] applied a mean-preserving transformation method to construct estimators for unknown parameters and functions and established their asymptotic normalities. We shall use the EL method to study the generalized functional-coefficient regression models with multiple smoothing variables when the response is subject to random right censoring. Assumption conditions and proofs of the main result are relegated to the Appendix

Methodology

Simulation Study