An Optimal Approach in Varying-Coe cient Models

One of the advantages for the varying-coeecient model is to allow the coeecients to vary as smooth functions of other variables and the model can be estimated easily through a simple local maximum likelihood method. This leads a simple one-step estimation procedure. We show that such a one-step method can not be optimal when some coeecient functions possess diierent degrees of smoothness. This drawback can be attenuated by using our proposed 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 idea case where the other coeecient function were known. A numerical study is carried out to illustrate the two-step method.