Modal regression statistical inference for longitudinal data semivarying coefficient models: Generalized estimating equations, empirical likelihood and variable selection

Abstract

Modal regression is a good alternative of the mean regression, because of its merits of both robustness and high inference efficiency. This paper is concerned with modal regression based statistical inference for semivarying coefficient models with longitudinal data, which include modal regression generalized estimating equations, modal regression empirical likelihood inference procedure for the parametric component and smooth- threshold modal regression generalized estimating equations for variable selection. These methods can incorporate the correlation structure of the longitudinal data and inherit the robustness and efficiency superiorities of the modal regression by choosing an appropriate data adaptive tuning parameter. Under mild conditions, the large sample theoretical properties are established. Simulation studies and real data analysis are also included to illustrate the finite sample performance.