Tests for the equality of conditional variance functions in nonparametric regression

In this paper we are interested in checking whether the conditional variances are equal in k ≥ 2 location-scale regression models. Our procedure is fully nonparametric and is based on the comparison of the error distributions under the null hypothesis of equality of variances and without making use...

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Autores: Pardo Fernández, Juan Carlos, Jiménez Gamero, María Dolores, El Ghouch, Anouar
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2015
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/42212
Acceso en línea:http://hdl.handle.net/11441/42212
https://doi.org/10.1214/15-EJS1058
Access Level:acceso abierto
Palabra clave:Asymptotics
Bootstrap
Comparison of curves
Empirical characteristic function
Empirical distribution function
Kernel smoothing
Local alternatives
Regression residuals
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spelling Tests for the equality of conditional variance functions in nonparametric regressionPardo Fernández, Juan CarlosJiménez Gamero, María DoloresEl Ghouch, AnouarAsymptoticsBootstrapComparison of curvesEmpirical characteristic functionEmpirical distribution functionKernel smoothingLocal alternativesRegression residualsIn this paper we are interested in checking whether the conditional variances are equal in k ≥ 2 location-scale regression models. Our procedure is fully nonparametric and is based on the comparison of the error distributions under the null hypothesis of equality of variances and without making use of this null hypothesis. We propose four test statistics based on empirical distribution functions (Kolmogorov-Smirnov and Cramèr-von Mises type test statistics) and two test statistics based on empirical characteristic functions. The limiting distributions of these six test statistics are established under the null hypothesis and under local alternatives. We show how to approximate the critical values using either an estimated version of the asymptotic null distribution or a bootstrap procedure. Simulation studies are conducted to assess the finite sample performance of the proposed tests. We also apply our tests to data on household expenditures.Ministerio de Economía y CompetitividadBelgian Science PolicyAcadémie universitaire LouvainInstitute of Mathematical StatisticsEstadística e Investigación OperativaMinisterio de Economía y Competitividad (MINECO). España2015info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttp://hdl.handle.net/11441/42212https://doi.org/10.1214/15-EJS1058reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésElectronic Journal of Statistics, 9 (2), 1826-1851.info:eu-repo/grantAgreement/MINECO/MTM2014-55966-P/P6/0311/16-039Shaker Heights (Ohio)info:eu-repo/semantics/openAccessoai:idus.us.es:11441/422122026-06-17T12:51:07Z
dc.title.none.fl_str_mv Tests for the equality of conditional variance functions in nonparametric regression
title Tests for the equality of conditional variance functions in nonparametric regression
spellingShingle Tests for the equality of conditional variance functions in nonparametric regression
Pardo Fernández, Juan Carlos
Asymptotics
Bootstrap
Comparison of curves
Empirical characteristic function
Empirical distribution function
Kernel smoothing
Local alternatives
Regression residuals
title_short Tests for the equality of conditional variance functions in nonparametric regression
title_full Tests for the equality of conditional variance functions in nonparametric regression
title_fullStr Tests for the equality of conditional variance functions in nonparametric regression
title_full_unstemmed Tests for the equality of conditional variance functions in nonparametric regression
title_sort Tests for the equality of conditional variance functions in nonparametric regression
dc.creator.none.fl_str_mv Pardo Fernández, Juan Carlos
Jiménez Gamero, María Dolores
El Ghouch, Anouar
author Pardo Fernández, Juan Carlos
author_facet Pardo Fernández, Juan Carlos
Jiménez Gamero, María Dolores
El Ghouch, Anouar
author_role author
author2 Jiménez Gamero, María Dolores
El Ghouch, Anouar
author2_role author
author
dc.contributor.none.fl_str_mv Estadística e Investigación Operativa
Ministerio de Economía y Competitividad (MINECO). España
dc.subject.none.fl_str_mv Asymptotics
Bootstrap
Comparison of curves
Empirical characteristic function
Empirical distribution function
Kernel smoothing
Local alternatives
Regression residuals
topic Asymptotics
Bootstrap
Comparison of curves
Empirical characteristic function
Empirical distribution function
Kernel smoothing
Local alternatives
Regression residuals
description In this paper we are interested in checking whether the conditional variances are equal in k ≥ 2 location-scale regression models. Our procedure is fully nonparametric and is based on the comparison of the error distributions under the null hypothesis of equality of variances and without making use of this null hypothesis. We propose four test statistics based on empirical distribution functions (Kolmogorov-Smirnov and Cramèr-von Mises type test statistics) and two test statistics based on empirical characteristic functions. The limiting distributions of these six test statistics are established under the null hypothesis and under local alternatives. We show how to approximate the critical values using either an estimated version of the asymptotic null distribution or a bootstrap procedure. Simulation studies are conducted to assess the finite sample performance of the proposed tests. We also apply our tests to data on household expenditures.
publishDate 2015
dc.date.none.fl_str_mv 2015
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11441/42212
https://doi.org/10.1214/15-EJS1058
url http://hdl.handle.net/11441/42212
https://doi.org/10.1214/15-EJS1058
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Electronic Journal of Statistics, 9 (2), 1826-1851.
info:eu-repo/grantAgreement/MINECO/MTM2014-55966-P/
P6/03
11/16-039
Shaker Heights (Ohio)
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Institute of Mathematical Statistics
publisher.none.fl_str_mv Institute of Mathematical Statistics
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.301603

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