Time：9:00am Nov.17,2017

Place：Room104,Building of Statistics of School

Reporter：Jiang Xuejun

Abstract：In this study, we propose a new test for heteroscedasticity of nonlinear regression models using a nonparametric statistic based on pairwise distances between points in a sample. The statistic can be formulated as a U statistic such that U-statistic theory can be applied. Although the limiting null distribution of the statistic is complicated, we derived a computationally feasible approximation for it.  The test can detect any local alternatives that are different from the null at a nearly optimal rate in hypothesis testing. The convergence rate of this test statistic does not depend on the dimension of the covariates, which greatly alleviates the impact of the curse of dimensionality. We include three simulation studies and two real data examples  to evaluate the performance of the test  and to demonstrate its applications.