Structure Identification, Estimation and Variable Selection for Varying Coefficient EV Models with Longitudinal Data

In this article, we propose a bias-corrected double penalized quadratic inference functions method to simultaneously identify model structure, estimate parameters, and perform variable selection for varying coefficient errors-in-variables (EV) models with longitudinal data. Unlike the linear models or the partial linear varying coefficient models, the proposed method does not assume in advance whether each regression coefficient is constant or varying. Instead, it represents each coefficient as a nonparametric function and identifies whether it is constant or varying using the proposed method. By employing a B-spline basis to approximate the unknown coefficient functions, the proposed method integrates a bias-corrected quadratic inference function with two penalized terms to achieve structure identification, estimation, and variable selection. Under certain regularized conditions, the consistency and sparsity properties of the estimator are established. Moreover, a three-step iterative algorithm is developed to implement the proposed method in practice. Simulation studies and a real data analysis demonstrate the superior finite-sample performance of the method.