报告题目： Pairwisedistance-based heteroscedasticity test for regressions
报 告 人： 蒋学军（南方科技大学数学系助理教授，副研究员）
Inthis paper, we propose a new test for heteroscedasticity of nonlinearregression models using a nonparametric statistic based on pairwise distancesbetween points in a sample. The statistic can be formulated as a U statisticsuch that U-statistic theory can be applied. Although the limiting nulldistribution of the statistic is complicated, we derive a computationallyfeasible approximation for it. The validity of the introduced bootstrapalgorithm is proven. The test can detect any local alternatives that aredifferent from the null at a nearly optimal rate in hypothesis testing. Theconvergence rate of this test statistic does not depend on the dimension of thecovariates, which greatly alleviates the impact of the curse of dimensionality.We include three simulation studies and two real data examples to evaluate theperformance of the test and to demonstrate its applications.