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 accountthe 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 forthe asymptotic variance and bias. Furthermore, a simulation study is conducted to evaluate the performance of the proposed method.