"Entropic CLT for Order Statistics" by Martina Cardone, Alex Dytso et al.
 

Entropic CLT for Order Statistics

Document Type

Conference Proceeding

Publication Date

1-1-2022

Abstract

It is well known that central order statistics exhibit a central limit behavior and converge to a Gaussian distribution as the sample size n grows. This paper strengthens this known result by establishing an entropic version of the central limit theorem (CLT) that ensures a stronger mode of convergence using the relative entropy. In particular, an order O(1/√ n) rate of convergence is established under mild conditions on the parent distribution of the sample generating the order statistics. To prove this result, ancillary results on order statistics are derived, which might be of independent interest.

Identifier

85136261897 (Scopus)

ISBN

[9781665421591]

Publication Title

IEEE International Symposium on Information Theory Proceedings

External Full Text Location

https://doi.org/10.1109/ISIT50566.2022.9834720

ISSN

21578095

First Page

718

Last Page

723

Volume

2022-June

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