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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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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DOI: https://doi.org/10.1007/s11749-017-0575-x
Keywords
- CLT
- Dependent random variables
- Breusch and Pagan test
- White’s test
- Heteroscedasticity
- Homoscedasticity
- High-dimensional regression
- Design matrix