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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, Cornell University.

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.

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Additional indexing

Item Type:Working Paper
Communities & Collections:03 Faculty of Economics > Department of Economics
Dewey Decimal Classification:330 Economics
JEL Classification:C1
Scope:Discipline-based scholarship (basic research)
Language:English
Date:July 2021
Deposited On:11 Feb 2022 12:28
Last Modified:06 Mar 2024 14:37
Series Name:ArXiv.org
Number of Pages:7
ISSN:2331-8422
OA Status:Green
Free access at:Official URL. An embargo period may apply.
Official URL:https://arxiv.org/abs/2107.10766
Other Identification Number:merlin-id:22116
  • Content: Published Version