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On the calculation of a robust S-estimator of a covariance matrix

✍ Scribed by N. A. Campbell; H. P. Lopuhaä; P. J. Rousseeuw

Publisher
John Wiley and Sons
Year
1998
Tongue
English
Weight
106 KB
Volume
17
Category
Article
ISSN
0277-6715

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✦ Synopsis

An S-estimator of multivariate location and scale minimizes the determinant of the covariance matrix, subject to a constraint on the magnitudes of the corresponding Mahalanobis distances. The relationship between S-estimators and w-estimators of multivariate location and scale can be used to calculate robust estimates of covariance matrices. Elemental subsets of observations are generated to derive initial estimates of means and covariances, and the w-estimator equations are then iterated until convergence to obtain the S-estimates. An example shows that converging to a (local) minimum from the initial estimates from the elemental subsets is an effective way of determining the overall minimum. None of the estimates gained from the elemental samples is close to the final solution.

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