Skip to Main content Skip to Navigation
Journal articles

A CLASS OF RENYI INFORMATION ESTIMATORS FOR MULTIDIMENSIONAL DENSITIES

Abstract : A class of estimators of the Rényi and Tsallis entropies of an unknown distribution f in R^m is presented. These estimators are based on the k-th nearest-neighbor distances computed from a sample of N i.i.d. vectors with distribution f. We show that entropies of any order q, including Shannon's entropy, can be estimated consistently with minimal assumptions on f. Moreover, we show that it is straightforward to extend the nearest-neighbor method to estimate the statistical distance between two distributions using one i.i.d. sample from each.
Complete list of metadatas

Cited literature [15 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-00331300
Contributor : Luc Pronzato <>
Submitted on : Thursday, October 16, 2008 - 11:21:26 AM
Last modification on : Tuesday, May 26, 2020 - 6:50:35 PM
Document(s) archivé(s) le : Monday, June 7, 2010 - 6:11:32 PM

File

AOS539.pdf
Publisher files allowed on an open archive

Identifiers

Collections

Citation

Nikolai Leonenko, Luc Pronzato, Vippal Savani. A CLASS OF RENYI INFORMATION ESTIMATORS FOR MULTIDIMENSIONAL DENSITIES. Annals of Statistics, Institute of Mathematical Statistics, 2008, 36 (5), pp.2153-2182. ⟨10.1214/07-AOS539⟩. ⟨hal-00331300⟩

Share

Metrics

Record views

396

Files downloads

321