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

Zhidong Bai (), Guangming Pan () and Yanqing Yin ()
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Zhidong Bai: Northeast Normal University
Guangming Pan: Nanyang Technological University
Yanqing Yin: Jiangsu Normal University

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2018, vol. 27, issue 4, No 11, 896-920

Abstract: 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.

Keywords: CLT; Dependent random variables; Breusch and Pagan test; White’s test; Heteroscedasticity; Homoscedasticity; High-dimensional regression; Design matrix; Primary 62J05; 62H15; Secondary 60F05 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s11749-017-0575-x

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