A central limit theorem for sums of functions of residuals in a high-dimensional regression model with an application to variance homoscedasticity test

TEST volume 27, pages896–920(2018)Cite this article

Abstract

We establish a joint central limit theorem for sums of squares and the fourth powers of residuals in a high-dimensional regression model. We then apply this CLT to detect the existence of heteroscedasticity for linear regression models without assuming randomness of covariates when the sample size n tends to infinity and the number of covariates p may be fixed or tend to infinity.

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Author information

Affiliations

  1. KLASMOE and School of Mathematics and Statistics, Northeast Normal University, Changchun, 130024, People’s Republic of China

    Zhidong Bai

  2. School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, 637371, Singapore

    Guangming Pan

  3. School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, 221116, People’s Republic of China

    Yanqing Yin

Authors
  1. Zhidong Bai
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  2. Guangming Pan
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  3. Yanqing Yin
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Corresponding author

Correspondence to Yanqing Yin.

Additional information

Zhidong Bai is partially supported by a Grant NSF China 11571067 and 11471140. Guangming Pan was partially supported by a MOE Tier 2 Grant 2014-T2-2-060 and by a MOE Tier 1 Grant RG25/14 at the Nanyang Technological University, Singapore. Yanqing Yin was partially supported by a Grant NSF China 11701234, the Priority Academic Program Development of Jiangsu Higher Education Institutions and a project of China Scholarship Council.

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Bai, Z., Pan, G. & Yin, Y. A central limit theorem for sums of functions of residuals in a high-dimensional regression model with an application to variance homoscedasticity test. TEST 27, 896–920 (2018). https://doi.org/10.1007/s11749-017-0575-x

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Keywords

  • CLT
  • Dependent random variables
  • Breusch and Pagan test
  • White’s test
  • Heteroscedasticity
  • Homoscedasticity
  • High-dimensional regression
  • Design matrix

Mathematics Subject Classification

  • Primary 62J05
  • 62H15
  • Secondary 60F05