The Annals of Statistics

Asymptotic Distributions of Multivariate Rank Order Statistics

Ludger Ruschendorf

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Abstract

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.

Article information

Source
Ann. Statist., Volume 4, Number 5 (1976), 912-923.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176343588

Digital Object Identifier
doi:10.1214/aos/1176343588

Mathematical Reviews number (MathSciNet)
MR420794

Zentralblatt MATH identifier
0359.62040

JSTOR
links.jstor.org

Subjects
Primary: 60F05: Central limit and other weak theorems
Secondary: 62G10: Hypothesis testing 60B10: Convergence of probability measures

Keywords
Multivariate invariance principles submartingale rank order process stronger metrics empirical process

Citation

Ruschendorf, Ludger. Asymptotic Distributions of Multivariate Rank Order Statistics. Ann. Statist. 4 (1976), no. 5, 912--923. doi:10.1214/aos/1176343588. https://projecteuclid.org/euclid.aos/1176343588


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Corrections

  • See Correction: L. Ruschendorf. Corrections: Asymptotic Distributions of Multivariate Rank Order Statistics. Ann. Statist., Volume 10, Number 4 (1982), 1311--1311.