Pairwise distance-based heteroscedasticity test for regressions  

作　　者：Xu Guo Xuejun Jiang Shumei Zhang Lixing Zhu 

机构地区：[1]School of Statistics,Beijing Normal University,Beijing 100875,China [2]Department of Statistics and Data Science,Southern University of Science and Technology,Shenzhen 518055,China [3]Department of Mathematics,Hong Kong Baptist University,Hong Kong,China

出　　处：《Science China Mathematics》2020年第12期2553-2572,共20页中国科学：数学（英文版）

基　　金：supported by Shenzhen Sci-Tech Fund(Grant No.JCYJ 20170307110329106);the Natural Science Foundation of Guangdong Province of China(Grant No.2016A030313856);National Natural Science Foundation of China(Grant Nos.11701034,11601227,11871263 and 11671042);the University Grants Council of Hong Kong。

摘　　要：In this study,we propose nonparametric testing for heteroscedasticity in nonlinear regression models based on pairwise distances between points in a sample.The test statistic can be formulated such that Ustatistic theory can be applied to it.Although the limiting null distribution of the statistic is complicated,we can derive a computationally feasible bootstrap approximation for such a distribution;the validity of the introduced bootstrap algorithm is proven.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 significantly alleviates the impact of dimensionality.We provide three simulation studies and a real-data example to evaluate the performance of the test and demonstrate its applications.

关 键 词：dimensionality heteroscedasticity testing pairwise distance U-statistic theory 

分 类 号：O212.1[理学—概率论与数理统计]