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.
|Original language||English (US)|
|Title of host publication||2022 IEEE International Symposium on Information Theory, ISIT 2022|
|Publisher||Institute of Electrical and Electronics Engineers Inc.|
|Number of pages||6|
|State||Published - 2022|
|Event||2022 IEEE International Symposium on Information Theory, ISIT 2022 - Espoo, Finland|
Duration: Jun 26 2022 → Jul 1 2022
|Name||2022 IEEE International Symposium on Information Theory (ISIT)|
|Conference||2022 IEEE International Symposium on Information Theory, ISIT 2022|
|Period||6/26/22 → 7/1/22|
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