Asymptotic independence of bivariate order statistics

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jun 2017Embargo end date: 01 Jan 2017 English Publisher:Elsevier BVJournal:Statistics & Probability Letters, volume 125, pages 91-98 (issn: 0167-7152,

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Authors: Michael Falk; Florian Wisheckel;

doi: 10.1016/j.spl.2017.01.020 , 10.48550/arxiv.1701.09108

arXiv: 1701.09108

Asymptotic independence of bivariate order statistics

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Abstract

It is well known that an extreme order statistic and a central order statistic (os) as well as an intermediate os and a central os from a sample of iid univariate random variables get asymptotically independent as the sample size increases. We extend this result to bivariate random variables, where the os are taken componentwise. An explicit representation of the conditional distribution of bivariate os turns out to be a powerful tool.

12 pages

Related Organizations

University of Würzburg
Germany

Keywords

intermediate order statistics, Asymptotic distribution theory in statistics, Primary 62G30, Secondary 60E05, 62H10, Mathematics - Statistics Theory, Statistics Theory (math.ST), Extreme value theory; extremal stochastic processes, multivariate order statistics, FOS: Mathematics, Order statistics; empirical distribution functions, copula, asymptotic independence

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