Robust Estimation of Multivariate Location and Scatter in the Presence of Missing Data

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Robust Estimation of Multivariate Location and Scatter in the Presence of Missing Data

TitleRobust Estimation of Multivariate Location and Scatter in the Presence of Missing Data
Publication TypeJournal Article
Year of Publication2012
AuthorsDanilov, M, Yohai, VJ, Zamar, RH
JournalJOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
Volume107
Pagination1178-1186
Date PublishedSEP
Type of ArticleArticle
ISSN0162-1459
KeywordsConsistent, Elliptical distribution, EM algorithm, Fixed point equation
AbstractTwo 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.
DOI10.1080/01621459.2012.699792