Inference on Varying-Coefficient Partially Linear Regression Model

The varying-coefficient partially linear regression model is proposed by combining nonparametric and varying-coefficient regression procedures. Wong, et al.(2008) proposed the model and gave its estimation by the local linear method. In this paper its inference is addressed. Based on these estimates, the generalized likelihood ratio test is established. Under the null hypotheses the normalized test statistic follows a χ2-distribution asymptotically, with the scale constant and the degrees of freedom being independent of the nuisance parameters. This is the Wilks phenomenon. Furthermore its asymptotic power is also derived, which achieves the optimal rate of convergence for nonparametric hypotheses testing. A simulation and a real example are used to evaluate the performances of the testing procedures empirically.