Model detection and estimation for single-index varying coefficient model

Single-index varying coefficient model (SIVCM) is a powerful tool for modeling nonlinearity in multivariate estimation, and has been widely used in the literature due to the fact that it can overcome the well-known phenomenon of “curse-of-dimensionality”. In this paper, we consider the problem of model detection and estimation for SIVCM. Based on the proposed combined penalization procedure, we can identify the true model structure consistently, and obtain a new semiparametric model—partially linear single-index varying coefficient model (PLSIVCM). Under the appropriate conditions, we demonstrate that the proposed penalized estimators of parametric and nonparametric components of PLSIVCM are consistent, but their asymptotic distributions are not available. Hence, we extend the minimum average variance estimation method to PLSIVCM, and establish the asymptotic normality for the refined estimators of index parameters, constant coefficients and varying coefficient functions, respectively. The finite sample performances of the proposed methods are illustrated by a Monte Carlo simulation study and the real data analysis.