Test On Heteroscedasticity In Functional Nonparametric Regression Model

It is of considerable interest in testing for heteroscedasticity in many practical studies. In recent years, functional data is very useful data, which is comprehensive. When functional data is used in practice, the first step is heteroscedasticity test.In this paper, the authors discuss this type of problem in framework of functional data regression models. A conditional test of nonparametric Monte Carlo Test is proposed and the empirical distribution function is constructed. The test is based on the approaches of nonparametric Monte Carlo Test. At last, the authors simulation the test method by a large number of examples, and show this method in the case of large sample to test the results are obvious.The advantages of nonparametric Monte Carlo Test are simple, intuition and programming easy. Theory of functional data is not comprehensive enough. And it is difficult to use traditional methods to construct test statistics. In this paper, we solve the problem by nonparametric Monte Carlo Test.