Estimation for a partially linear single-index varying-coefficient model

Abstract

In this paper, we study the estimation for the partial linear single-index varying-coefficient model, which is a natural extension of the partially linear varying-coefficient model. A stepwise estimation procedure is developed to obtain asymptotic normality estimators of the index parameter vector, the coefficient parameter vector, and the coefficient function vector. The asymptotic properties of the resulting estimators are established under some conditions. A simulation study is conducted to assess the performance of the stepwise estimation procedure and the results show that our proposed procedure performs well in finite samples. Furthermore, a real data example is also used to illustrate our proposed method.