cient Estimation and Inferences forVarying - Coe cient Models

This paper deals with statistical inferences based on the varying-coeecient models proposed by Hastie and Tibshirani (1993). Local polynomial regression techniques are used to estimate coeecient functions and the asymptotic normality of the resulting estimators is established. The standard error formulas for estimated coeecients 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 coeecient functions in a varying-coeecient model are constant or whether any covariates are statistically signiicant 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 one-step 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. We would like to thank the Editor, the Associate Editor and two referees for their constructive and detailed suggestions that led to improving signiicantly the presentation of the paper.