Robust and efficient estimation of multivariate scatter and location

Several equivariant estimators of multivariate location and scatter are studied, which are highly robust, have a controllable finite-sample efficiency and are computationally feasible in large dimensions. The most frequently employed estimators are not quite satisfactory in this respect. The Minimum...

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Autor principal:	Maronna, Ricardo Antonio
Publicado:	2017
Materias:	Kullback–Leibler divergence MM-estimator S-estimator Stahel–Donoho estimator τ-estimator Multivariable systems Sampling Efficient estimation Equivariant estimators Minimum covariance determinant Minimum volume ellipsoids Outlier Detection S-estimators Simulation studies Efficiency
Acceso en línea:	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01679473_v109_n_p64_Maronna http://hdl.handle.net/20.500.12110/paper_01679473_v109_n_p64_Maronna
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	paper:paper_01679473_v109_n_p64_Maronna
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spelling	paper:paper_01679473_v109_n_p64_Maronna2023-06-08T15:17:07Z Robust and efficient estimation of multivariate scatter and location Maronna, Ricardo Antonio Kullback–Leibler divergence MM-estimator S-estimator Stahel–Donoho estimator τ-estimator Multivariable systems Sampling Efficient estimation Equivariant estimators Minimum covariance determinant Minimum volume ellipsoids MM-estimator Outlier Detection S-estimators Simulation studies Efficiency Several equivariant estimators of multivariate location and scatter are studied, which are highly robust, have a controllable finite-sample efficiency and are computationally feasible in large dimensions. The most frequently employed estimators are not quite satisfactory in this respect. The Minimum Volume Ellipsoid (MVE) and the Minimum Covariance Determinant (MCD) estimators are known to have a very low efficiency. S-estimators with a monotonic weight function like the bisquare have a low efficiency when the dimension p is small, and their efficiency tends to one with increasing p. Unfortunately, this advantage is outweighed by a serious loss in robustness for large p. Four families of estimators with controllable efficiencies whose performance for moderate to large p has not been explored to date are studied: S-estimators with a non-monotonic weight function, MM-estimators, τ-estimators, and the Stahel–Donoho estimator. Two types of starting estimators are employed: the MVE computed through subsampling, and a semi-deterministic procedure previously proposed for outlier detection, based on the projections with maximum and minimum kurtosis. A simulation study shows that an S-estimator with non-monotonic weight function can simultaneously attain high efficiency and high robustness for p≥15, while an MM-estimator with a particular weight function can be recommended for p>15. For both recommended estimators, the initial values are given by the semi-deterministic procedure mentioned above. © 2016 Elsevier B.V. Fil:Maronna, R.A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2017 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01679473_v109_n_p64_Maronna http://hdl.handle.net/20.500.12110/paper_01679473_v109_n_p64_Maronna
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	Kullback–Leibler divergence MM-estimator S-estimator Stahel–Donoho estimator τ-estimator Multivariable systems Sampling Efficient estimation Equivariant estimators Minimum covariance determinant Minimum volume ellipsoids MM-estimator Outlier Detection S-estimators Simulation studies Efficiency
spellingShingle	Kullback–Leibler divergence MM-estimator S-estimator Stahel–Donoho estimator τ-estimator Multivariable systems Sampling Efficient estimation Equivariant estimators Minimum covariance determinant Minimum volume ellipsoids MM-estimator Outlier Detection S-estimators Simulation studies Efficiency Maronna, Ricardo Antonio Robust and efficient estimation of multivariate scatter and location
topic_facet	Kullback–Leibler divergence MM-estimator S-estimator Stahel–Donoho estimator τ-estimator Multivariable systems Sampling Efficient estimation Equivariant estimators Minimum covariance determinant Minimum volume ellipsoids MM-estimator Outlier Detection S-estimators Simulation studies Efficiency
description	Several equivariant estimators of multivariate location and scatter are studied, which are highly robust, have a controllable finite-sample efficiency and are computationally feasible in large dimensions. The most frequently employed estimators are not quite satisfactory in this respect. The Minimum Volume Ellipsoid (MVE) and the Minimum Covariance Determinant (MCD) estimators are known to have a very low efficiency. S-estimators with a monotonic weight function like the bisquare have a low efficiency when the dimension p is small, and their efficiency tends to one with increasing p. Unfortunately, this advantage is outweighed by a serious loss in robustness for large p. Four families of estimators with controllable efficiencies whose performance for moderate to large p has not been explored to date are studied: S-estimators with a non-monotonic weight function, MM-estimators, τ-estimators, and the Stahel–Donoho estimator. Two types of starting estimators are employed: the MVE computed through subsampling, and a semi-deterministic procedure previously proposed for outlier detection, based on the projections with maximum and minimum kurtosis. A simulation study shows that an S-estimator with non-monotonic weight function can simultaneously attain high efficiency and high robustness for p≥15, while an MM-estimator with a particular weight function can be recommended for p>15. For both recommended estimators, the initial values are given by the semi-deterministic procedure mentioned above. © 2016 Elsevier B.V.
author	Maronna, Ricardo Antonio
author_facet	Maronna, Ricardo Antonio
author_sort	Maronna, Ricardo Antonio
title	Robust and efficient estimation of multivariate scatter and location
title_short	Robust and efficient estimation of multivariate scatter and location
title_full	Robust and efficient estimation of multivariate scatter and location
title_fullStr	Robust and efficient estimation of multivariate scatter and location
title_full_unstemmed	Robust and efficient estimation of multivariate scatter and location
title_sort	robust and efficient estimation of multivariate scatter and location
publishDate	2017
url	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01679473_v109_n_p64_Maronna http://hdl.handle.net/20.500.12110/paper_01679473_v109_n_p64_Maronna
work_keys_str_mv	AT maronnaricardoantonio robustandefficientestimationofmultivariatescatterandlocation
_version_	1768543365956108288

Robust and efficient estimation of multivariate scatter and location

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