Statistical Estimation in Varying-Coe cient Models

Varying-coe cient models are a useful extension of the classical linear models. The appeal of these models is that the coe cient functions can easily be estimated via a simple local regression. This yields a simple one-step estimation procedure. We show that such a one-step method can not be optimal when di erent coe cient functions admit di erent degrees of smoothness. This drawback can be repaired by using our proposed two-step estimation procedure. The asymptotic mean-squared errors for the two-step procedure is obtained and is shown to achieve the optimal rate of convergence. A few simulation studies show that the gain by the two-step procedure can be quite substantial. The methodology is illustrated by an application to an environmental dataset.