Dimension-Free Anticoncentration Bounds for Gaussian Order Statistics with Discussion of Applications to Multiple Testing

Damian Kozbur

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arXiv · 2107.10766

Dimension-Free Anticoncentration Bounds for Gaussian Order Statistics with Discussion of Applications to Multiple Testing

Damian Kozbur

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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 $\varepsilon$ is bounded above by $2{\varepsilon}k ({ 1+\mathrm{E}[\|X\|_\infty ]}) $. This bound has implications for generalized error rate control in statistical high-dimensional multiple hypothesis testing problems, which are discussed subsequently.

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Damian Kozbur. 2021-07-22. Dimension-Free Anticoncentration Bounds for Gaussian Order Statistics with Discussion of Applications to Multiple Testing. https://arxiv.org/abs/2107.10766

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