Robust estimation of multivariate location and scatter in the presence of missing data

Two main issues regarding data quality are data contamination (outliers) and data completion (missing data). These two problems have attracted much attention and research but surprisingly, they are seldom considered together. Popular robust methods such as S-estimators of multivariate location and s...

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Guardado en:
Detalles Bibliográficos
Publicado: 2012
Materias:
Consistent
Elliptical distribution
EM algorithm
Fixed point equation
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01621459_v107_n499_p1178_Danilov
http://hdl.handle.net/20.500.12110/paper_01621459_v107_n499_p1178_Danilov
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_01621459_v107_n499_p1178_Danilov
record_format dspace
spelling paper:paper_01621459_v107_n499_p1178_Danilov2023-06-08T15:13:38Z Robust estimation of multivariate location and scatter in the presence of missing data Consistent Elliptical distribution EM algorithm Fixed point equation Two main issues regarding data quality are data contamination (outliers) and data completion (missing data). These two problems have attracted much attention and research but surprisingly, they are seldom considered together. Popular robust methods such as S-estimators of multivariate location and scatter offer protection against outliers but cannot deal with missing data, except for the obviously inefficient approach of deleting all incomplete cases. We generalize the definition of S-estimators of multivariate location and scatter to simultaneously deal with missing data and outliers. We show that the proposed estimators are strongly consistent under elliptical models when data are missing completely at random. We derive an algorithm similar to the Expectation-Maximization algorithm for computing the proposed estimators. This algorithm is initialized by an extension for missing data of the minimum volume ellipsoid. We assess the performance of our proposal by Monte Carlo simulation and give some real data examples. This article has supplementary material online. © 2012 American Statistical Association. 2012 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01621459_v107_n499_p1178_Danilov http://hdl.handle.net/20.500.12110/paper_01621459_v107_n499_p1178_Danilov
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Consistent
Elliptical distribution
EM algorithm
Fixed point equation
spellingShingle Consistent
Elliptical distribution
EM algorithm
Fixed point equation
Robust estimation of multivariate location and scatter in the presence of missing data
topic_facet Consistent
Elliptical distribution
EM algorithm
Fixed point equation
description Two main issues regarding data quality are data contamination (outliers) and data completion (missing data). These two problems have attracted much attention and research but surprisingly, they are seldom considered together. Popular robust methods such as S-estimators of multivariate location and scatter offer protection against outliers but cannot deal with missing data, except for the obviously inefficient approach of deleting all incomplete cases. We generalize the definition of S-estimators of multivariate location and scatter to simultaneously deal with missing data and outliers. We show that the proposed estimators are strongly consistent under elliptical models when data are missing completely at random. We derive an algorithm similar to the Expectation-Maximization algorithm for computing the proposed estimators. This algorithm is initialized by an extension for missing data of the minimum volume ellipsoid. We assess the performance of our proposal by Monte Carlo simulation and give some real data examples. This article has supplementary material online. © 2012 American Statistical Association.
title Robust estimation of multivariate location and scatter in the presence of missing data
title_short Robust estimation of multivariate location and scatter in the presence of missing data
title_full Robust estimation of multivariate location and scatter in the presence of missing data
title_fullStr Robust estimation of multivariate location and scatter in the presence of missing data
title_full_unstemmed Robust estimation of multivariate location and scatter in the presence of missing data
title_sort robust estimation of multivariate location and scatter in the presence of missing data
publishDate 2012
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01621459_v107_n499_p1178_Danilov
http://hdl.handle.net/20.500.12110/paper_01621459_v107_n499_p1178_Danilov
_version_ 1768541650609504256

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