Multivariate location estimation using extension of R-estimates through U-statistics type approach

Chaudhuri, Probal (1992) Multivariate location estimation using extension of R-estimates through U-statistics type approach The Annals of Statistics, 20 (2). pp. 897-916. ISSN 0090-5364

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Official URL: http://www.jstor.org/stable/10.2307/2241989

Abstract

We consider a class of U-statistics type estimates for multivariate location. The estimates extend some R-estimates to multivariate data. In particular, the class of estimates includes the multivariate median considered by Gini and Galvani (1929) and Haldane (1948) and a multivariate extension of the well-known Hodges-Lehmann (1963) estimate. We explore large sample behavior of these estimates by deriving a Bahadur type representation for them. In the process of developing these asymptotic results, we observe some interesting phenomena that closely resemble the famous shrinkage phenomenon observed by Stein (1956) in high dimensions. Interestingly, the phenomena that we observe here occur even in dimension d = 2.

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ID Code:74617
Deposited On:17 Dec 2011 10:08
Last Modified:17 Dec 2011 10:08

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