"Entropic Central Limit Theorem for Order Statistics" by Martina Cardone, Alex Dytso et al.
 

Entropic Central Limit Theorem for Order Statistics

Document Type

Article

Publication Date

4-1-2023

Abstract

It is well known that central order statistics exhibit a central limit behavior and converge to a Gaussian distribution as the sample size grows. This paper strengthens this known result by establishing an entropic version of the central limit theorem that ensures a stronger mode of convergence using the relative entropy. This upgrade in convergence is shown at the expense of extra regularity conditions, which can be considered as mild. To prove this result, ancillary results on order statistics are derived, which might be of independent interest. For instance, a rather general bound on the moments of order statistics, and an upper bound on the mean squared error of estimating the p (0,1) -th quantile of an unknown cumulative distribution function, are derived. Finally, a discussion on the necessity of the derived conditions for convergence and on the rate of convergence and monotonicity of the relative entropy is provided.

Identifier

85141619285 (Scopus)

Publication Title

IEEE Transactions on Information Theory

External Full Text Location

https://doi.org/10.1109/TIT.2022.3219344

e-ISSN

15579654

ISSN

00189448

First Page

2193

Last Page

2205

Issue

4

Volume

69

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