Inference for Nonparametric Parts in Single-Index Varying-Coefficient Model

Xia and Li (1999) proposed the single-index varying-coefficient model (SIVCM), which is frequently used in statistical modeling. However, the inference for the SIVCM has not been very well developed. In this article, our main purpose is to examine whether the generalized likelihood ratio (GLR) test is applicable to the testing problem for the nonparametric parts of the SIVCMs. Under the null hypothesis the newly proposed GLR statistic asymptotically follows the chi-squared distribution with scale constant and degree of freedom independent of the nuisance parameters or functions. A new Wilks phenomenon is unveiled. A simulated example is given to evaluate our proposed methods.