Weighted empirical likelihood for heteroscedastic varying coefficient partially non‐linear models with missing data

• Published in: Stat (International Statistical Institute) 2021-12, Vol.10 (1), p.n/a
• Main Authors: Fan, Guo‐Liang, Wang, Lu‐Lu, Xu, Hong‐Xia
• Format: Article
• Language: English
• Subjects: Coefficients; empirical likelihood; heteroscedastic error; inverse probability weighted technique; Likelihood ratio; Mathematical models; Missing data; Parameters; varying coefficient partially non‐linear model
• ISSN: 2049-1573; 2049-1573
• DOI: 10.1002/sta4.353

In this article, a weighted empirical likelihood technique for constructing the empirical likelihood confidence regions is applied to study the heteroscedastic varying coefficient partially non‐linear models with missing response data. We first provide an estimator of the error variance based on the Nadaraya–Watson kernel estimation method. Then a weighted empirical log‐likelihood ratio of the unknown parameter is constructed based on the inverse probability weighted technique. The maximum empirical likelihood (MEL) estimator of the unknown parameter is obtained. Further, a weighted empirical log‐likelihood ratio of the varying coefficient function is introduced based on the MEL estimator and the inverse probability weighted method. The limiting distributions of the resulting statistics for both the unknown parameter and varying coefficient function are shown to have the standard chi‐squared distribution. A simulation study and a real data set example are undertaken to investigate the finite sample performance of the proposed methods.