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.
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.
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.
| Item Type: | Working Paper |
|---|---|
| Communities & Collections: | 03 Faculty of Economics > Department of Economics |
| Dewey Decimal Classification: | 330 Economics |
| JEL Classification: | C1 |
| Language: | English |
| Date: | July 2021 |
| Deposited On: | 11 Feb 2022 12:28 |
| Last Modified: | 06 Sep 2022 08:10 |
| 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 |
Kozbur, Damian