Inference on coefficient function for varying-coefficient partially linear model

One important model in handling the multivariate data is the varying-coefficient partially linear regression model. In this paper, the generalized likelihood ratio test is developed to test whether its coefficient functions are varying or not. It is showed that the normalized proposed test follows asymptotically χ ²-distribution and theWilks phenomenon under the null hypothesis, and its asymptotic power achieves the optimal rate of the convergence for the nonparametric hypotheses testing. Some simulation studies illustrate that the test works well.