Testing heteroscedasticity for regression models based on projections

Falong Tan, Xuejun Jiang*, Xu Guo, Lixing Zhu

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

4 Citations (Scopus)

Abstract

We propose a new test for heteroscedasticity in parametric and partial linear regression models in multidimensional spaces. When the dimension of the covariates is large, or even moderate, existing tests for heteroscedasticity perform badly, owing to the "curse of dimensionality." To address this problem, we construct a test for heteroscedasticity that uses a projection-based empirical process. Then, we study the asymptotic properties of the test statistic under the null and alternative hypotheses. The results show that the test detects the departure of local alternatives from the null hypothesis at the fastest possible rate during hypothesis testing. Because the limiting null distribution of the test statistic is not asymptotically distribution free, we propose a residual-based bootstrap approach and investigate the validity of its approximations. Simulations verify the finite-sample performance of the test. Two real-data analyses are conducted to demonstrate the proposed test.

Original languageEnglish
Pages (from-to)625-646
Number of pages22
JournalStatistica Sinica
Volume31
Issue number2
DOIs
Publication statusPublished - Apr 2021

Scopus Subject Areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

User-Defined Keywords

  • Heteroscedasticity testing
  • Partial linear models
  • Projection
  • U-process

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