Multivariate Order Statistics: The Intermediate Case

TL;DR

This paper extends the known asymptotic normality of intermediate order statistics from univariate cases to multivariate vectors, considering componentwise order statistics in arbitrary dimensions.

Contribution

It generalizes the asymptotic normality results for intermediate order statistics to multivariate settings with arbitrary dimensions.

Findings

Asymptotic normality holds for multivariate intermediate order statistics.

The generalization applies to vectors in any dimension.

Componentwise order statistics exhibit similar asymptotic behavior as univariate cases.

Abstract

Asymptotic normality of intermediate order statistics taken from univariate iid random variables is well-known. We generalize this result to random vectors in arbitrary dimension, where the order statistics are taken componentwise.