Multivariate Location Estimation Using Extension of $R$-Estimates Through $U$-Statistics Type Approach
Chaudhuri, Probal
Ann. Statist., Tome 20 (1992) no. 1, p. 897-916 / Harvested from Project Euclid
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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 $d = 2$.
Publié le : 1992-06-14
Classification:  $R$-estimates,  multivariate median,  Hodges-Lehmann estimate,  $U$-statistics,  generalized order statistics,  Bahadur representation,  Stein phenomenon,  62G05,  62G20,  62H12,  62E20,  62H10 
@article{1176348662,
     author = {Chaudhuri, Probal},
     title = {Multivariate Location Estimation Using Extension of $R$-Estimates Through $U$-Statistics Type Approach},
     journal = {Ann. Statist.},
     volume = {20},
     number = {1},
     year = {1992},
     pages = { 897-916},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176348662}
}

Chaudhuri, Probal. Multivariate Location Estimation Using Extension of $R$-Estimates Through $U$-Statistics Type Approach. Ann. Statist., Tome 20 (1992) no. 1, pp.  897-916. http://gdmltest.u-ga.fr/item/1176348662/