Asymptotic Independence of Bivariate Order Statistics

2017/01/31 by Michael Falk, Falk, Michael, Florian Wisheckel +1
Economics, Econometrics and Finance · Environmental Science · Mathematics · #62H10 #FOS: Mathematics #Financial Risk and Volatility Modeling #Hydrology and Drought Analysis #Primary 62G30 #Secondary 60E05 #Statistical Distribution Estimation and Applications #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1701.09108

openalex publication_date 2017/01/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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