Estimators for the common principal components model based on reweighting: Influence functions and Monte Carlo study

The common principal components model for several groups of multivariate observations is a useful parsimonious model for the scatter structure which assumes equal principal axes but different variances along those axes for each group. Due to the lack of resistance of the classical maximum likelihood...

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Detalles Bibliográficos
Autores principales:	Boente, G., Pires, A.M., Rodrigues, I.M.
Formato:	JOUR
Materias:	Common principal components Outlier detection Projection-Pursuit Reweighted estimators Robust estimation
Acceso en línea:	http://hdl.handle.net/20.500.12110/paper_00261335_v67_n2_p189_Boente
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

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spelling	todo:paper_00261335_v67_n2_p189_Boente2023-10-03T14:36:52Z Estimators for the common principal components model based on reweighting: Influence functions and Monte Carlo study Boente, G. Pires, A.M. Rodrigues, I.M. Common principal components Outlier detection Projection-Pursuit Reweighted estimators Robust estimation The common principal components model for several groups of multivariate observations is a useful parsimonious model for the scatter structure which assumes equal principal axes but different variances along those axes for each group. Due to the lack of resistance of the classical maximum likelihood estimators for the parameters of this model, several robust estimators have been proposed in the literature: plug-in estimators and projection-pursuit (PP) type estimators. In this paper, we show that it is possible to improve the low efficiency of the projection-pursuit estimators by applying a reweighting step. More precisely, we consider plug-in estimators obtained by plugging a reweighted estimator of the scatter matrices into the maximum likelihood equations defining the principal axes. The weights considered penalize observations with large values of the influence measures defined by Boente et al. (2002). The new estimators are studied in terms of theoretical properties (influence functions and asymptotic variances) and are compared with other existing estimators in a simulation study. © 2007 Springer-Verlag. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00261335_v67_n2_p189_Boente
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	Common principal components Outlier detection Projection-Pursuit Reweighted estimators Robust estimation
spellingShingle	Common principal components Outlier detection Projection-Pursuit Reweighted estimators Robust estimation Boente, G. Pires, A.M. Rodrigues, I.M. Estimators for the common principal components model based on reweighting: Influence functions and Monte Carlo study
topic_facet	Common principal components Outlier detection Projection-Pursuit Reweighted estimators Robust estimation
description	The common principal components model for several groups of multivariate observations is a useful parsimonious model for the scatter structure which assumes equal principal axes but different variances along those axes for each group. Due to the lack of resistance of the classical maximum likelihood estimators for the parameters of this model, several robust estimators have been proposed in the literature: plug-in estimators and projection-pursuit (PP) type estimators. In this paper, we show that it is possible to improve the low efficiency of the projection-pursuit estimators by applying a reweighting step. More precisely, we consider plug-in estimators obtained by plugging a reweighted estimator of the scatter matrices into the maximum likelihood equations defining the principal axes. The weights considered penalize observations with large values of the influence measures defined by Boente et al. (2002). The new estimators are studied in terms of theoretical properties (influence functions and asymptotic variances) and are compared with other existing estimators in a simulation study. © 2007 Springer-Verlag.
format	JOUR
author	Boente, G. Pires, A.M. Rodrigues, I.M.
author_facet	Boente, G. Pires, A.M. Rodrigues, I.M.
author_sort	Boente, G.
title	Estimators for the common principal components model based on reweighting: Influence functions and Monte Carlo study
title_short	Estimators for the common principal components model based on reweighting: Influence functions and Monte Carlo study
title_full	Estimators for the common principal components model based on reweighting: Influence functions and Monte Carlo study
title_fullStr	Estimators for the common principal components model based on reweighting: Influence functions and Monte Carlo study
title_full_unstemmed	Estimators for the common principal components model based on reweighting: Influence functions and Monte Carlo study
title_sort	estimators for the common principal components model based on reweighting: influence functions and monte carlo study
url	http://hdl.handle.net/20.500.12110/paper_00261335_v67_n2_p189_Boente
work_keys_str_mv	AT boenteg estimatorsforthecommonprincipalcomponentsmodelbasedonreweightinginfluencefunctionsandmontecarlostudy AT piresam estimatorsforthecommonprincipalcomponentsmodelbasedonreweightinginfluencefunctionsandmontecarlostudy AT rodriguesim estimatorsforthecommonprincipalcomponentsmodelbasedonreweightinginfluencefunctionsandmontecarlostudy
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Estimators for the common principal components model based on reweighting: Influence functions and Monte Carlo study

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