Profile Statistical Inference for Partially Linear Additive Models with a Diverging Number of Parameters

Abstract

This paper considers partially linear additive models with the number of parameters diverging when some linear constraints on the parametric part are available. This paper proposes a constrained profile least-squares estimation for the parametric components with the nonparametric functions being estimated by basis function approximations. The consistency and asymptotic normality of the restricted estimator are given under some certain conditions. The authors construct a profile likelihood ratio test statistic to test the validity of the linear constraints on the parametric components, and demonstrate that it follows asymptotically chi-squared distribution under the null and alternative hypotheses. The finite sample performance of the proposed method is illustrated by simulation studies and a data analysis.