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
Recommended Citation
Cardone, Martina; Dytso, Alex; and Rush, Cynthia, "Entropic CLT for Order Statistics" (2022). Faculty Publications. 3336.
https://digitalcommons.njit.edu/fac_pubs/3336