Empirical likelihood for varying coefficient partially nonlinear model with missing responses

AIMS Mathematics

Xiuli Wang¹  Liqi Xia¹  Peixin Zhao²  Yunquan Song³ 

[1] 1. School of Mathematics and Statistics, Shandong Normal University, Jinan 250358, China;2. College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China;3. College of Science, China University of Petroleum, Qingdao 266580, China;

关键词: varying coefficient partially nonlinear model;    profile nonlinear least squares estimation;    weighted imputation;    missing responses;    empirical likelihood inferences;    confidence region;   

DOI  :  10.3934/math.2021418

来源: DOAJ

【 摘 要 】

In this paper, we consider the statistical inferences for varying coefficient partially nonlinear model with missing responses. Firstly, we employ the profile nonlinear least squares estimation based on the weighted imputation method to estimate the unknown parameter and the nonparametric function, meanwhile the asymptotic normality of the resulting estimators is proved. Secondly, we consider empirical likelihood inferences based on the weighted imputation method for the unknown parameter and nonparametric function, and propose an empirical log-likelihood ratio function for the unknown parameter vector in the nonlinear function and a residual-adjusted empirical log-likelihood ratio function for the nonparametric component, meanwhile construct relevant confidence regions. Thirdly, the response mean estimation is also studied. In addition, simulation studies are conducted to examine the finite sample performance of our methods, and the empirical likelihood approach based on the weighted imputation method (IEL) is further applied to a real data example.

【 授权许可】

Unknown