A new orthogonality empirical likelihood for varying coefficient partially linear instrumental variable models with longitudinal data

Varying coefficient partially linear models are usually used for longitudinal data analysis, and an interest is mainly to improve efficiency of regression coefficients. By the orthogonality estimation technology and the empirical likelihood inference method, we propose a new orthogonality-based empirical likelihood inference method to estimate parameter and nonparametric components in a class of varying coefficient partially linear instrumental variable models with longitudinal data. The proposed procedure can separately estimate the parametric and nonparametric components, and the resulting estimators do not affect each other. Under some mild conditions, we establish some asymptotic properties of the resulting estimators. Furthermore, the finite sample performance of the proposed procedure is assessed by some simulation experiments and a real data analysis.