scholarly journals Jackknifing for partially linear varying-coefficient errors-in-variables model with missing response at random

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Yuye Zou ◽  
Chengxin Wu
Keyword(s):  
Normal Approximation ◽  
Likelihood Method ◽  
Errors In Variables ◽  
Missing Response ◽  
Varying Coefficient ◽  
Partially Linear ◽  
Coverage Probabilities ◽  
Interval Lengths ◽  
Mean Square Errors ◽  
Jackknife Empirical Likelihood

Abstract In this paper, we focus on the response mean of the partially linear varying-coefficient errors-in-variables model with missing response at random. A simulation study is conducted to compare jackknife empirical likelihood method with normal approximation method in terms of coverage probabilities and average interval lengths, and a comparison of the proposed estimators is done based on their biases and mean square errors.

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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