Penalised empirical likelihood for semiparametric varying-coefficient partially linear errors-in-variables models

2021 ◽  
pp. 1-19
Author(s):  
Li Yan ◽  
Junwei He ◽  
Xia Chen
Keyword(s):  
Empirical Likelihood ◽  
Errors In Variables ◽  
Varying Coefficient ◽  
Partially Linear

scholarly journals Block Empirical Likelihood for Semiparametric Varying-Coefficient Partially Linear Errors-in-Variables Models with Longitudinal Data

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Yafeng Xia ◽  
Hu Da
Keyword(s):  
Longitudinal Data ◽  
Likelihood Ratio ◽  
Empirical Likelihood ◽  
Likelihood Ratio Statistic ◽  
Likelihood Inference ◽  
Errors In Variables ◽  
Varying Coefficient ◽  
Mild Conditions ◽  
Partially Linear ◽  
Log Likelihood

Block empirical likelihood inference for semiparametric varying-coeffcient partially linear errors-in-variables models with longitudinal data is investigated. We apply the block empirical likelihood procedure to accommodate the within-group correlation of the longitudinal data. The block empirical log-likelihood ratio statistic for the parametric component is suggested. And the nonparametric version of Wilk’s theorem is derived under mild conditions. Simulations are carried out to access the performance of the proposed procedure.

scholarly journals Statistical Inference for the Heteroscedastic Partially Linear Varying-Coefficient Errors-in-Variables Model with Missing Censoring Indicators

2021 ◽  
Vol 2021 ◽  
pp. 1-26
Author(s):  
Yuye Zou ◽  
Chengxin Wu
Keyword(s):  
Empirical Likelihood ◽  
Error Variance ◽  
Variance Function ◽  
Likelihood Method ◽  
Coefficient Function ◽  
Errors In Variables ◽  
Finite Sample ◽  
Right Censored Data ◽  
Varying Coefficient ◽  
Partially Linear

In this paper, we focus on heteroscedastic partially linear varying-coefficient errors-in-variables models under right-censored data with censoring indicators missing at random. Based on regression calibration, imputation, and inverse probability weighted methods, we define a class of modified profile least square estimators of the parameter and local linear estimators of the coefficient function, which are applied to constructing estimators of the error variance function. In order to improve the estimation accuracy and take into account the heteroscedastic error, reweighted estimators of the parameter and coefficient function are developed. At the same time, we apply the empirical likelihood method to construct confidence regions and maximum empirical likelihood estimators of the parameter. Under appropriate assumptions, the asymptotic normality of the proposed estimators is studied. The strong uniform convergence rate for the estimators of the error variance function is considered. Also, the asymptotic chi-squared distribution of the empirical log-likelihood ratio statistics is proved. A simulation study is conducted to evaluate the finite sample performance of the proposed estimators. Meanwhile, one real data example is provided to illustrate our methods.

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