Measuring dependencies of order statistics: An information theoretic perspective
Document Type
Conference Proceeding
Publication Date
4-11-2021
Abstract
This work considers a random sample X1,X2,...,Xn drawn independently and identically distributed from some known parent distribution PX with X(1) ≤ X(2) ≤ ... ≤ X(n) being the order statistics of the sample. Under the assumption of an invertible cumulative distribution function associated with the parent distribution PX, a distribution-free property is established showing that the f-divergence between the joint distribution of order statistics and the product distribution of order statistics does not depend on PX. Moreover, it is shown that the mutual information between two subsets of order statistics also satisfies a distribution-free property; that is, it does not depend on PX. Furthermore, the decoupling rates between X(r) and X(m) (i.e., rates at which the mutual information approaches zero) are characterized for various choices of (r,m). The work also considers discrete distributions, which do not satisfy the previously-stated invertibility assumption, and it is shown that no such distribution-free property holds: the mutual information between order statistics does depend on the parent distribution PX. Upper bounds on the decoupling rates in the discrete setting are also established.
Identifier
85113332546 (Scopus)
ISBN
[9781728159621]
Publication Title
2020 IEEE Information Theory Workshop Itw 2020
External Full Text Location
https://doi.org/10.1109/ITW46852.2021.9457617
Grant
CCF-1849757
Fund Ref
National Science Foundation
Recommended Citation
Dytso, Alex; Cardone, Martina; and Rush, Cynthia, "Measuring dependencies of order statistics: An information theoretic perspective" (2021). Faculty Publications. 4180.
https://digitalcommons.njit.edu/fac_pubs/4180
