Testing the constancy in varying-coefficient regression models

Two hypothesis testing problems are considered in this paper to check the constancy of the coefficients in the varying-coefficient regression model. Tests for the two corresponding hypothesis testing problems are derived by two p-values. The proposed p-values can be thought as the generalized p-values, which are given by linear interpolation based on fiducial method. When all of the coefficients are constants, the p-value is uniformly distributed on interval (0, 1). Furthermore, the bound of the difference between the cumulative distribution function of the p-value and the uniform distribution on (0, 1) is given, which tends to 0 under some conditions. Meanwhile, the proposed tests are proved to be consistent under mild conditions. In addition, the proposed new method could be extended to include a broader range of hypotheses. Some good finite sample performances of the tests are investigated by simulations, in which a comparison with other test is given. Finally, a simple example based on real data is given to illustrate the application of our test, different result was obtained based on the proposed test.