Efficient Estimation and Inferences for Varying-Coefficient Models

This paper deals with statistical inferences based on the varying-coe cient models proposed by Local polynomial regression techniques are used to estimate coe cient functions and the asymptotic normality of the resulting estimators is established. The standard error formulas for estimated coe cients are derived and are empirically tested. A goodness-of-t test technique, based on a nonparametric maximum likelihood ratio type of test, is also proposed to detect whether certain coe cient functions in a varying-coe cient model are constant or whether any covariates are statistically signi cant in the model. The null distribution of the test is estimated by a conditional bootstrap method. Our estimation techniques involve solving hundreds of local likelihood equations. To reduce computational burden, a onestep Newton-Raphson estimator is proposed and implemented. We show that the resulting one-step procedure can save computational cost in an order of tens without deteriorating its performance, both asymptotically and empirically. Both simulated and real data examples are used to illustrate our proposed methodology.