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February 2001 Regularity and Uniqueness for Constrained M-Estimates and Redescending M-Estimates
John T. Kent, David E. Tyler
Ann. Statist. 29(1): 252-265 (February 2001). DOI: 10.1214/aos/996986508


Constrained M-estimates of multivariate location and scatter are found by finding the global minimum of an objective function subject to a constraint. They are related to redescending M-estimates of multivariate location and scatter since any stationary point of the objective function corresponds to such an M-estimate. Unfortunately, even for the population form of the estimator, that is, the constrained M-functional, the objective function may have multiple stationary points. In this paper, we give conditions under which the objective function is as well behaved as possible, in particular that it has at most one local minimum. To carry out this task, we introduce a class of distributions which we call "regular" distributions with respect to a particular objective function.


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John T. Kent. David E. Tyler. "Regularity and Uniqueness for Constrained M-Estimates and Redescending M-Estimates." Ann. Statist. 29 (1) 252 - 265, February 2001.


Published: February 2001
First available in Project Euclid: 5 August 2001

zbMATH: 1029.62029
MathSciNet: MR1833965
Digital Object Identifier: 10.1214/aos/996986508

Primary: 62F35 , 62H10
Secondary: 60E07

Keywords: elliptic symmetry , Infinite divisibility , M-estimates , Schur concavity

Rights: Copyright © 2001 Institute of Mathematical Statistics


Vol.29 • No. 1 • February 2001
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