Pairwise distance-based heteroscedasticity test for regressions

Xu Guo, Xuejun Jiang*, Shumei Zhang, Lixing Zhu

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

5 Citations (Scopus)


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 U-statistic 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.

Original languageEnglish
Pages (from-to)2553–2572
Number of pages20
JournalScience China Mathematics
Issue number12
Early online date18 Jun 2020
Publication statusPublished - Dec 2020

Scopus Subject Areas

  • Mathematics(all)

User-Defined Keywords

  • 62G08
  • 62G20
  • dimensionality
  • heteroscedasticity testing
  • pairwise distance
  • U-statistic theory


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