# Dimension-free anticoncentration bounds for Gaussian order statistics with discussion of applications to multiple testing

Kozbur, Damian (2021). Dimension-free anticoncentration bounds for Gaussian order statistics with discussion of applications to multiple testing. arXiv.org 2107.10766, University of Zurich.

## Abstract

The following anticoncentration property is proved. The probability that the k-order statistic of an arbitrarily correlated jointly Gaussian random vector X with unit variance components lies within an interval of length ε is bounded above by 2εk(1 + E[‖X‖∞ ]). This bound has implications for generalized error rate control in statistical high-dimensional multiple hypothesis testing problems, which are discussed subsequently.

## Abstract

The following anticoncentration property is proved. The probability that the k-order statistic of an arbitrarily correlated jointly Gaussian random vector X with unit variance components lies within an interval of length ε is bounded above by 2εk(1 + E[‖X‖∞ ]). This bound has implications for generalized error rate control in statistical high-dimensional multiple hypothesis testing problems, which are discussed subsequently.