Open Access
June 1996 Constrained M-estimation for multivariate location and scatter
John T. Kent, David E. Tyler
Ann. Statist. 24(3): 1346-1370 (June 1996). DOI: 10.1214/aos/1032526973


Consider the problem of estimating the location vector and scatter matrix from a set of multivariate data. Two standard classes of robust estimates are M-estimates and S-estimates. The M-estimates can be tuned to give good local robustness properties, such as good efficiency and a good bound on the influence function at an underlying distribution such as the multivariate normal. However, M-estimates suffer from poor breakdown properties in high dimensions. On the other hand, S-estimates can be tuned to have good breakdown properties, but when tuned in this way, they tend to suffer from poor local robustness properties. In this paper a hybrid estimate called a constrained M-estimate is proposed which combines both good local and good global robustness properties.


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John T. Kent. David E. Tyler. "Constrained M-estimation for multivariate location and scatter." Ann. Statist. 24 (3) 1346 - 1370, June 1996.


Published: June 1996
First available in Project Euclid: 20 September 2002

zbMATH: 0862.62048
MathSciNet: MR1401854
Digital Object Identifier: 10.1214/aos/1032526973

Primary: 62F35 , 62H12

Keywords: $M$-estimates , $S$-estimates , Breakdown , robustness

Rights: Copyright © 1996 Institute of Mathematical Statistics

Vol.24 • No. 3 • June 1996
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