Two-Step Likelihood Estimation Procedure for Varying-Coefficient Models

One of the advantages for the varying-coefficient model is to allow the coefficients to vary as smooth functions of other variables and the model can be estimated easily through a simple local quasi-likelihood method. This leads to a simple one-step estimation procedure. We show that such a one-step method cannot be optimal when some coefficient functions possess different degrees of smoothness. This drawback can be attenuated by using a two-step estimation approach. The asymptotic normality and mean-squared errors of the two-step method are obtained and it is also shown that the two-step estimation not only achieves the optimal convergent rate but also shares the same optimality as the ideal case where the other coefficient functions were known. A numerical study is carried out to illustrate the two-step method.