The Behavior of the Stahel-Donoho Robust Multivariate Estimator

The Stahel-Donoho estimators (t, V) of multivariate location and scatter are defined as a weighted mean and a weighted covariance matrix with weights of the form w(r), where w is a weight function and r is a measure of "outlyingness," obtained by considering all univariate projections of t...

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Bibliographic Details
Published in:Journal of the American Statistical Association 1995-03, Vol.90 (429), p.330-341
Main Authors: Maronna, Ricardo A., Yohai, Víctor J.
Format: Article
Language:English
Subjects:
Bias robustness
Covariance
Covariance matrices
Datasets
Distribution
Estimation bias
Estimators
Exact sciences and technology
Forecasts
Mathematics
Maximum likelihood estimation
Multivariate analysis
Multivariate location scatter
Outliers
Point estimators
Point masses
Probability and statistics
Projection methods
Sciences and techniques of general use
Statistical median
Statistics
Theory and Methods
Weighting functions
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Summary:The Stahel-Donoho estimators (t, V) of multivariate location and scatter are defined as a weighted mean and a weighted covariance matrix with weights of the form w(r), where w is a weight function and r is a measure of "outlyingness," obtained by considering all univariate projections of the data. It has a high breakdown point for all dimensions and order √n consistency. The asymptotic bias of V for point mass contamination for suitable weight functions is compared with that of Rousseeuw's minimum volume ellipsoid (MVE) estimator. A simulation shows that for a suitable w, t and V exhibit high efficiency for both normal and Cauchy distributions and are better than their competitors for normal data with point-mass contamination. The performances of the estimators for detecting outliers are compared for both a real and a synthetic data set.
ISSN:0162-1459
1537-274X
DOI:10.1080/01621459.1995.10476517