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June, 1992 Multivariate Location Estimation Using Extension of $R$-Estimates Through $U$-Statistics Type Approach
Probal Chaudhuri
Ann. Statist. 20(2): 897-916 (June, 1992). DOI: 10.1214/aos/1176348662

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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Probal Chaudhuri. "Multivariate Location Estimation Using Extension of $R$-Estimates Through $U$-Statistics Type Approach." Ann. Statist. 20 (2) 897 - 916, June, 1992. https://doi.org/10.1214/aos/1176348662

Information

Published: June, 1992
First available in Project Euclid: 12 April 2007

zbMATH: 0762.62013
MathSciNet: MR1165598
Digital Object Identifier: 10.1214/aos/1176348662

Subjects:
Primary: 62G05
Secondary: 62E20, 62G20, 62H10, 62H12

Rights: Copyright © 1992 Institute of Mathematical Statistics

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Vol.20 • No. 2 • June, 1992
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