Robust and efficient estimation of multivariate scatter and location

Ricardo A. Maronna and Victor J. Yohai

Computational Statistics & Data Analysis, 2017, vol. 109, issue C, 64-75

Abstract: 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.

Keywords: MM-estimator; τ-estimator; S-estimator; Stahel–Donoho estimator; Kullback–Leibler divergence (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167947316302705
Full text for ScienceDirect subscribers only.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:109:y:2017:i:c:p:64-75

DOI: 10.1016/j.csda.2016.11.006

Access Statistics for this article

Computational Statistics & Data Analysis is currently edited by S.P. Azen

More articles in Computational Statistics & Data Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().