Empirical likelihood for semivarying coefficient model with measurement error in the nonparametric part

Abstract

A semivarying coefficient model with measurement error in the nonparametric part was proposed by Feng and Xue (Ann Inst Stat Math 66:121–140, 2014), but its inferences have not been systematically studied. This paper applies empirical likelihood method to construct confidence regions/intervals for the regression parameter and coefficient function. When some auxiliary information about the parametric part is available, the empirical log-likelihood ratio statistic for the regression parameter is introduced based on the corrected local linear estimator of the coefficient function. Furthermore, corrected empirical log-likelihood ratio statistic for coefficient function is also investigated with the use of auxiliary information. The limiting distributions of the resulting statistics both for the regression parameter and coefficient function are shown to have standard Chi-squared distribution. Simulation experiments and a real data set are presented to evaluate the finite sample performance of our proposed method.