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

Author

Listed:
  • Zhidong Bai

    (Northeast Normal University)

  • Guangming Pan

    (Nanyang Technological University)

  • Yanqing Yin

    (Jiangsu Normal University)

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.

Suggested Citation

  • Zhidong Bai & Guangming Pan & Yanqing Yin, 2018. "A central limit theorem for sums of functions of residuals in a high-dimensional regression model with an application to variance homoscedasticity test," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(4), pages 896-920, December.
    • Handle: RePEc:spr:testjl:v:27:y:2018:i:4:d:10.1007_s11749-017-0575-x
    DOI: 10.1007/s11749-017-0575-x
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    References listed on IDEAS

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    1. H. Dette & A. Munk, 1998. "Testing heteroscedasticity in nonparametric regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(4), pages 693-708.
    2. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    3. Breusch, T S & Pagan, A R, 1979. "A Simple Test for Heteroscedasticity and Random Coefficient Variation," Econometrica, Econometric Society, vol. 47(5), pages 1287-1294, September.
    4. Liu, Huan & Tang, Yongqiang & Zhang, Hao Helen, 2009. "A new chi-square approximation to the distribution of non-negative definite quadratic forms in non-central normal variables," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 853-856, February.
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    Cited by:

    1. Rui Wang & Xingzhong Xu, 2021. "A Bayesian-motivated test for high-dimensional linear regression models with fixed design matrix," Statistical Papers, Springer, vol. 62(4), pages 1821-1852, August.
    2. Zhenhong Huang & Chen Wang & Jianfeng Yao, 2023. "The First-stage F Test with Many Weak Instruments," Papers 2302.14423, arXiv.org, revised Sep 2024.

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