Orthogonality-based bias-corrected empirical likelihood inference for partial linear varying coefficient EV models with longitudinal data

In this paper, we study the model estimation for the partial linear varying coefficient errors-in-variables (EV) models with longitudinal data. Based on the empirical likelihood and quadratic inference functions (QIF), we propose an orthogonality-based bias-corrected empirical likelihood estimation method using the orthogonal decomposition (QR) method of matrix. The proposed method can handle the measurement errors of covariates and unknown within-subject correlation simultaneously, estimate the parametric and nonparametric components separately. Under some regularity conditions, the resulting estimator of the parametric component is asymptotic normal and the estimators of the nonparametric varying coefficients achieve the optimal convergence rate. Furthermore, we conduct simulation studies and a real data analysis to compare the performance of the proposed method and existing methods in finite samples. The results show that the feasibility of the proposed method is obvious.