Generalized Empirical Likelihood Inference in Partially Linear Errors-in-Variables Models with Longitudinal data

Abstract

This article is concerned with estimations for longitudinal partial linear models with covariate that is measured with error. We propose a generalized empirical likelihood method by combining correction attenuation and quadratic inference functions. The method takes into account the within-subject correlation without involving direct estimation of nuisance parameters in the correlation matrix. We define a generalized empirical likelihood-based statistic for the regression coefficients and residual adjusted empirical likelihood for the baseline function.The empirical log-likelihood ratios are proven to be asymptotically chi-squared, and the corresponding confidence regions are then constructed. Compared with methods based on normal approximations, the generalized empirical likelihood does not require consistent estimators for the asymptotic variance and bias. Furthermore, a simulation study is conducted to evaluate the performance of the proposed method.