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September, 1976 Asymptotic Distributions of Multivariate Rank Order Statistics
Ludger Ruschendorf
Ann. Statist. 4(5): 912-923 (September, 1976). DOI: 10.1214/aos/1176343588


By means of a general weak convergence theorem some invariance principles are proven for the multivariate sequential empirical process and for the multivariate rank order process w.r.t. stronger metrics than the generalized Skorohod metric. The underlying random variables are neither assumed to be independent nor to be stationary. These results are then applied to derive convergence of the weighted empirical cumulatives and for the weighted rank order process. Finally by a new representation asymptotic normality is proven for a general class of linear multivariate rank order statistics.


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Ludger Ruschendorf. "Asymptotic Distributions of Multivariate Rank Order Statistics." Ann. Statist. 4 (5) 912 - 923, September, 1976.


Published: September, 1976
First available in Project Euclid: 12 April 2007

zbMATH: 0359.62040
MathSciNet: MR420794
Digital Object Identifier: 10.1214/aos/1176343588

Primary: 60F05
Secondary: 60B10 , 62G10

Keywords: empirical process , Invariance principles , multivariate , rank order process , stronger metrics , submartingale

Rights: Copyright © 1976 Institute of Mathematical Statistics

Vol.4 • No. 5 • September, 1976
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