Robust discrimination under a hierarchy on the scatter matrices

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Under normality, Flury and Schmid [Quadratic discriminant functions with constraints on the covariances matrices: some asymptotic results, J. Multivariate Anal. 40 (1992) 244-261] investigated the asymptotic properties of the quadratic discrimination procedure under hierarchical models for the scatt...

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Autores principales: Bianco, A., Boente, G., Pires, A.M., Rodrigues, I.M.
Formato: Artículo publishedVersion
Lenguaje:Inglés
Publicado: 2008
Materias:
Common principal components
Outliers
Partial influence functions
Plug-in methods
Proportional scatter matrices
Quadratic discrimination
Robust estimation
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_0047259X_v99_n6_p1332_Bianco
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling paperaa:paper_0047259X_v99_n6_p1332_Bianco2023-06-12T16:45:41Z Robust discrimination under a hierarchy on the scatter matrices J. Multivariate Anal. 2008;99(6):1332-1357 Bianco, A. Boente, G. Pires, A.M. Rodrigues, I.M. Common principal components Outliers Partial influence functions Plug-in methods Proportional scatter matrices Quadratic discrimination Robust estimation Under normality, Flury and Schmid [Quadratic discriminant functions with constraints on the covariances matrices: some asymptotic results, J. Multivariate Anal. 40 (1992) 244-261] investigated the asymptotic properties of the quadratic discrimination procedure under hierarchical models for the scatter matrices, that is: (i) arbitrary scatter matrices, (ii) common principal components, (iii) proportional scatter matrices and (iv) identical matrices. In this paper, we study the properties of robust quadratic discrimination rules based on robust estimates of the involved parameters. Our analysis is based on the partial influence functions of the functionals related to these parameters and allows to derive the asymptotic variances of the estimated coefficients under models (i)-(iv). From them, we conclude that the asymptotic variances verify the same order relations as those obtained by Flury and Schmid [Quadratic discriminant functions with constraints on the covariances matrices: some asymptotic results, J. Multivariate Anal. 40 (1992) 244-261] for the classical estimators. We also perform a Monte Carlo study for different sample sizes and different hierarchies which shows the advantage of using robust procedures over classical ones, when anomalous data are present. It also confirms that better rates of misclassification can be achieved if a more parsimonious model among all the correct ones is used instead of the standard quadratic discrimination. © 2007 Elsevier Inc. All rights reserved. Fil:Bianco, A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Boente, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2008 info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion application/pdf eng info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_0047259X_v99_n6_p1332_Bianco
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
language Inglés
orig_language_str_mv eng
topic Common principal components
Outliers
Partial influence functions
Plug-in methods
Proportional scatter matrices
Quadratic discrimination
Robust estimation
spellingShingle Common principal components
Outliers
Partial influence functions
Plug-in methods
Proportional scatter matrices
Quadratic discrimination
Robust estimation
Bianco, A.
Boente, G.
Pires, A.M.
Rodrigues, I.M.
Robust discrimination under a hierarchy on the scatter matrices
topic_facet Common principal components
Outliers
Partial influence functions
Plug-in methods
Proportional scatter matrices
Quadratic discrimination
Robust estimation
description Under normality, Flury and Schmid [Quadratic discriminant functions with constraints on the covariances matrices: some asymptotic results, J. Multivariate Anal. 40 (1992) 244-261] investigated the asymptotic properties of the quadratic discrimination procedure under hierarchical models for the scatter matrices, that is: (i) arbitrary scatter matrices, (ii) common principal components, (iii) proportional scatter matrices and (iv) identical matrices. In this paper, we study the properties of robust quadratic discrimination rules based on robust estimates of the involved parameters. Our analysis is based on the partial influence functions of the functionals related to these parameters and allows to derive the asymptotic variances of the estimated coefficients under models (i)-(iv). From them, we conclude that the asymptotic variances verify the same order relations as those obtained by Flury and Schmid [Quadratic discriminant functions with constraints on the covariances matrices: some asymptotic results, J. Multivariate Anal. 40 (1992) 244-261] for the classical estimators. We also perform a Monte Carlo study for different sample sizes and different hierarchies which shows the advantage of using robust procedures over classical ones, when anomalous data are present. It also confirms that better rates of misclassification can be achieved if a more parsimonious model among all the correct ones is used instead of the standard quadratic discrimination. © 2007 Elsevier Inc. All rights reserved.
format Artículo
Artículo
publishedVersion
author Bianco, A.
Boente, G.
Pires, A.M.
Rodrigues, I.M.
author_facet Bianco, A.
Boente, G.
Pires, A.M.
Rodrigues, I.M.
author_sort Bianco, A.
title Robust discrimination under a hierarchy on the scatter matrices
title_short Robust discrimination under a hierarchy on the scatter matrices
title_full Robust discrimination under a hierarchy on the scatter matrices
title_fullStr Robust discrimination under a hierarchy on the scatter matrices
title_full_unstemmed Robust discrimination under a hierarchy on the scatter matrices
title_sort robust discrimination under a hierarchy on the scatter matrices
publishDate 2008
url http://hdl.handle.net/20.500.12110/paper_0047259X_v99_n6_p1332_Bianco
work_keys_str_mv AT biancoa robustdiscriminationunderahierarchyonthescattermatrices
AT boenteg robustdiscriminationunderahierarchyonthescattermatrices
AT piresam robustdiscriminationunderahierarchyonthescattermatrices
AT rodriguesim robustdiscriminationunderahierarchyonthescattermatrices
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