# Asymptotic Independence of Bivariate Order Statistics

## TL;DR

This paper extends the known asymptotic independence of certain univariate order statistics to bivariate cases, providing explicit representations of their conditional distributions.

## Contribution

It generalizes asymptotic independence results to bivariate order statistics and introduces explicit conditional distribution representations.

## Key findings

- Asymptotic independence holds for bivariate order statistics.
- Explicit formulas for conditional distributions are derived.
- Results extend univariate asymptotic independence to bivariate cases.

## 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.