Local polynomial fitting in semivarying coefficient models

Varying coefficient models are useful extensions of the classical linear models. Under the condition that the coefficient functions possess about the same degrees of smoothness, the model can easily be estimated via simple local regression.. This leads to the one-step estimation procedure. In this paper, we consider a semivarying coefficient model which is an extension of the varying coefficient model, which is called the semivarying-coefficient model. Procedures for estimation of the linear part and the nonparametric part are developed and their associated statistical properties are studied. The proposed methods are illustrated by some simulation studies and a real example.