Identification of Non-Varying Coefficients in Varying-Coefficient Models

Abstract

A partially varying-coefficient model is one of the useful modelling tools. In this model, some coefficients of a linear model are kept to be constant whilst the others are allowed to vary with another factor. However, rarely can the analysts know a priori which coefficients can be assumed to be constant and which ones are varying with the given factor. Therefore, the identification problem of the constant coefficients should be solved before the partially varying-coefficient model is used to analyze a real-world data set. In this article, a simple test method is proposed to achieve this task, in which the test statistic is constructed as the sample variance of the estimates of each coefficient function in a well-known varying-coefficient model. Moreover two procedures, called F -approximation and three-moment χ 2 approximation, are employed to derive the p-value of the test. Furthermore, some simulations are conducted to examine the performance of the test and the results are satisfactory.