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Redescending $M$-Estimates of Multivariate Location and Scatter

John T. Kent, David E. Tyler

The Annals of Statistics · 1991 · Volume 19 · Issue 4

DOI: 10.1214/aos/1176348388

Abstract

A class of redescending $M$-estimates of multivariate location and scatter are investigated. Sufficient conditions are given to ensure the existence and uniqueness of the estimates. These results are applied to the multivariate $t$-distribution with degrees of freedom $\nu \geq 1.$

Keywords

62H10; 62H12; multivariate $t$-distribution; Redescending $M$-estimate; robustness;

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