Testing homoscedasticity of a large number of population

Given k populations and assuming that independent samples are available from each of them, the problem of testing for the equality of the k population variances is addressed. In contrast to the classical setting, where k is kept fixed and the sample size from each population increases without bound,...

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Autores principales:	Jiménez-Gamero, María Dolores, Valdora, Marina, Rodríguez, Daniela
Formato:	Artículo
Lenguaje:	Inglés
Publicado:	Statistical Papers (e-ISSN 1613-9798) 2025
Materias:	Matemáticas y estadística Mathematics and statistics Estadística Statistics
Acceso en línea:	https://repositorio.utdt.edu/handle/20.500.13098/13446
Aporte de:	Repositorio Digital Universidad Torcuato Di Tella de Universidad Torcuato Di Tella

id	I57-R163-20.500.13098-13446
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spelling	I57-R163-20.500.13098-134462025-06-07T05:03:15Z Testing homoscedasticity of a large number of population Jiménez-Gamero, María Dolores Valdora, Marina Rodríguez, Daniela Matemáticas y estadística Mathematics and statistics Estadística Statistics Given k populations and assuming that independent samples are available from each of them, the problem of testing for the equality of the k population variances is addressed. In contrast to the classical setting, where k is kept fixed and the sample size from each population increases without bound, here k is assumed to be large and the size of each sample small in comparison to k. A new test is proposed. The asymptotic distribution of the test statistic is stated under the null hypothesis of equality of the k variances as well as under alternatives, which allows us to study the consistency of the test. Specifically, it is shown that the test statistic is asymptotically free distributed under the null hypothesis. Two bootstrap approximations to the null distribution of the test statistic are also investigated. The finite sample performance of the test based on the asymptotic null distribution and on the two bootstrap approximations, is studied via simulation. The proposal is applied to a real data set. Statistical Papers (e-ISSN 1613-9798) 2025-06-06T19:27:30Z 2025 info:eu-repo/semantics/article https://repositorio.utdt.edu/handle/20.500.13098/13446 eng Statistical Papers (e-ISSN 1613-9798), 66, 32 (2025) info:eu-repo/semantics/restrictedAccess http://rightsstatements.org/page/InC/1.0/?language=es 25 p. application/pdf application/pdf
institution	Universidad Torcuato Di Tella
institution_str	I-57
repository_str	R-163
collection	Repositorio Digital Universidad Torcuato Di Tella
language	Inglés
orig_language_str_mv	eng
topic	Matemáticas y estadística Mathematics and statistics Estadística Statistics
spellingShingle	Matemáticas y estadística Mathematics and statistics Estadística Statistics Jiménez-Gamero, María Dolores Valdora, Marina Rodríguez, Daniela Testing homoscedasticity of a large number of population
topic_facet	Matemáticas y estadística Mathematics and statistics Estadística Statistics
description	Given k populations and assuming that independent samples are available from each of them, the problem of testing for the equality of the k population variances is addressed. In contrast to the classical setting, where k is kept fixed and the sample size from each population increases without bound, here k is assumed to be large and the size of each sample small in comparison to k. A new test is proposed. The asymptotic distribution of the test statistic is stated under the null hypothesis of equality of the k variances as well as under alternatives, which allows us to study the consistency of the test. Specifically, it is shown that the test statistic is asymptotically free distributed under the null hypothesis. Two bootstrap approximations to the null distribution of the test statistic are also investigated. The finite sample performance of the test based on the asymptotic null distribution and on the two bootstrap approximations, is studied via simulation. The proposal is applied to a real data set.
format	Artículo
author	Jiménez-Gamero, María Dolores Valdora, Marina Rodríguez, Daniela
author_facet	Jiménez-Gamero, María Dolores Valdora, Marina Rodríguez, Daniela
author_sort	Jiménez-Gamero, María Dolores
title	Testing homoscedasticity of a large number of population
title_short	Testing homoscedasticity of a large number of population
title_full	Testing homoscedasticity of a large number of population
title_fullStr	Testing homoscedasticity of a large number of population
title_full_unstemmed	Testing homoscedasticity of a large number of population
title_sort	testing homoscedasticity of a large number of population
publisher	Statistical Papers (e-ISSN 1613-9798)
publishDate	2025
url	https://repositorio.utdt.edu/handle/20.500.13098/13446
work_keys_str_mv	AT jimenezgameromariadolores testinghomoscedasticityofalargenumberofpopulation AT valdoramarina testinghomoscedasticityofalargenumberofpopulation AT rodriguezdaniela testinghomoscedasticityofalargenumberofpopulation
_version_	1842217771696390144

Testing homoscedasticity of a large number of population

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