Efficient estimation and inferences for varying-coefficient models

This article deals with statistical inferences based on the varying-coeffic ient models proposed by Hastie and Tibshirani. Local polynomial regression techniques are used to estimate coefficient functions, and the asymptotic n ormality of the resulting estimators is established. The standard error for mulas far estimated coefficients are derived and are empirically tested. A goodness-of-fit test technique, based on a nonparametric maximum likelihood ratio type of test, is also proposed to detect whether certain coefficient functions in a varying-coefficient model are constant or whether any covar iates are statistically significant in the model. The null distribution of the test is estimated by a conditional bootstrap method. Our estimation tec hniques involve solving hundreds of local likelihood equations. To reduce t he computational burden, a one-step Newton-Raphson estimator is proposed an d implemented. The resulting one-step procedure is shown to save computatio nal cost on an order of tens with no deterioration in performance, both asy mptotically and empirically. Both simulated and real data examples are used to illustrate our proposed methodology.