M-estimation and B-spline approximation for varying coefficient models with longitudinal data

A global smoothing procedure is developed using B-spline function approximations for estimating the unknown functions of a varying coefficient model with repeated measurements. A general formulation is used to treat mean, median, quantile and robust mean regressions in one setting. The global convergence rates of the M-estimators of unknown coefficient functions are established. The asymptotic distributes of M-estimators are derived and the approximate confidence intervals are also established. Various applications of the main results, including estimating conditional quantile coefficient functions and robustifying the mean regression coefficient functions are given. Finite sample properties of our procedures are studied through Monte Carlo simulations.