Statistical inference for semiparametric varying-coefficient partially linear models with a diverging number of components

Abstract

In applications, other than sample information, some prior information on parameters can be used to improve the estimation efficiency. In the framework of varying-coefficient partially linear models with the number of parametric and nonparametric components diverging, this paper proposes a restricted profile least-squares estimation for the parametric components after the varying coefficients are estimated by basis function approximations. This estimator is shown to be consistent and asymptotically normal under certain regularity conditions. To check the validity of the linear constraints on the parametric components, we construct a profile generalized likelihood ratio test statistic and demonstrate that it follows asymptotically chi-squared distribution under the null and alternative hypotheses. Simulation studies are conducted and the Boston housing data is analyzed to illustrate the proposed method.