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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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

id	sg-ntu-dr.10356-142678
record_format	dspace
spelling	sg-ntu-dr.10356-1426782020-06-26T07:48:45Z A central limit theorem for sums of functions of residuals in a high-dimensional regression model with an application to variance homoscedasticity test Bai, Zhidong Pan, Guangming Yin, Yanqing School of Physical and Mathematical Sciences Science::Mathematics CLT Dependent Random Variables 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. MOE (Min. of Education, S’pore) 2020-06-26T07:48:45Z 2020-06-26T07:48:45Z 2017 Journal Article Bai, Z., Pan, G., & Yin, Y. (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, 27(4), 896-920. doi:10.1007/s11749-017-0575-x 1133-0686 https://hdl.handle.net/10356/142678 10.1007/s11749-017-0575-x 2-s2.0-85038820493 4 27 896 920 en TEST © 2017 Sociedad de Estadística e Investigación Operativa. All rights reserved.
institution	Nanyang Technological University
building	NTU Library
country	Singapore
collection	DR-NTU
language	English
topic	Science::Mathematics CLT Dependent Random Variables
spellingShingle	Science::Mathematics CLT Dependent Random Variables Bai, Zhidong Pan, Guangming Yin, Yanqing A central limit theorem for sums of functions of residuals in a high-dimensional regression model with an application to variance homoscedasticity test
description	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.
author2	School of Physical and Mathematical Sciences
author_facet	School of Physical and Mathematical Sciences Bai, Zhidong Pan, Guangming Yin, Yanqing
format	Article
author	Bai, Zhidong Pan, Guangming Yin, Yanqing
author_sort	Bai, Zhidong
title	A central limit theorem for sums of functions of residuals in a high-dimensional regression model with an application to variance homoscedasticity test
title_short	A central limit theorem for sums of functions of residuals in a high-dimensional regression model with an application to variance homoscedasticity test
title_full	A central limit theorem for sums of functions of residuals in a high-dimensional regression model with an application to variance homoscedasticity test
title_fullStr	A central limit theorem for sums of functions of residuals in a high-dimensional regression model with an application to variance homoscedasticity test
title_full_unstemmed	A central limit theorem for sums of functions of residuals in a high-dimensional regression model with an application to variance homoscedasticity test
title_sort	central limit theorem for sums of functions of residuals in a high-dimensional regression model with an application to variance homoscedasticity test
publishDate	2020
url	https://hdl.handle.net/10356/142678
_version_	1681058438956711936

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

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