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
Recommended Citation
Cardone, Martina; Dytso, Alex; and Rush, Cynthia, "Entropic Central Limit Theorem for Order Statistics" (2023). Faculty Publications. 1812.
https://digitalcommons.njit.edu/fac_pubs/1812