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

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

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...

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Bibliographic Details
Main Authors: Bai, Zhidong, Pan, Guangming, Yin, Yanqing
Other Authors: School of Physical and Mathematical Sciences
Format: Article
Language:English
Published: 2020
Subjects:
Science::Mathematics
CLT
Dependent Random Variables
Online Access:https://hdl.handle.net/10356/142678
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Institution: Nanyang Technological University
Language: English
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Summary: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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