Generalized Empirical Likelihood for Partially Linear Errors‐in‐Variables Regression Model With Longitudinal Data
针对纵向数据中参数和非参数部分协变量均存在测量误差的部分线性模型，提出一种考虑组内相关性的广义经验似然方法，无需直接估计相关矩阵中的冗余参数，并证明了经验似然比的渐近卡方分布。
ABSTRACT In this paper, we study the generalized empirical likelihood inference for a partially linear model with measurement errors in both the covariates of parametric and nonparametric parts, on the basis of longitudinal data. The proposed generalized empirical likelihood approach considers within‐group correlations to estimate regression coefficients and does not involve direct estimation of nuisance parameters in the correlation matrix. At the true parameter, the empirical ‐likelihood ratio is proved to be asymptotically chi‐square distributed under regularity conditions, and the corresponding confidence intervals are constructed. Next, the profile EL ratios for the parameter are given, and it is verified that these ratios follow the chi‐square distribution. Furthermore, the strong consistency and the convergence rate for the estimator of a nonparametric function are obtained, and the ‐consistency of the estimator of is verified. The performance of the proposed method is verified by numerical simulation and real data analysis.