publication . Other literature type . Article . 1992

Multivariate Location Estimation Using Extension of $R$-Estimates Through $U$-Statistics Type Approach

Probal Chaudhuri;
Open Access English
  • Published: 01 Jun 1992
  • Publisher: The Institute of Mathematical Statistics
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 phenom...
Subjects
free text keywords: $R$-estimates, multivariate median, Hodges-Lehmann estimate, $U$-statistics, generalized order statistics, Bahadur representation, Stein phenomenon, 62G05, 62G20, 62H12, 62E20, 62H10, Statistics, Probability and Uncertainty, Statistics and Probability, Statistics, Order statistic, Hodges–Lehmann estimator, Asymptotic analysis, Econometrics, Multivariate normal distribution, Location parameter, Mathematics, U-statistic, Multivariate statistics
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publication . Other literature type . Article . 1992

Multivariate Location Estimation Using Extension of $R$-Estimates Through $U$-Statistics Type Approach

Probal Chaudhuri;