A class of Rényi information estimators for multidimensional densities

Leonenko, Nikolai N. ORCID: https://orcid.org/0000-0003-1932-4091, Pronzato, Luc and Savani, Vippal 2008. A class of Rényi information estimators for multidimensional densities. Annals of Statistics 36 (5) , pp. 2153-2182. 10.1214/07-AOS539

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Abstract

A class of estimators of the Rényi and Tsallis entropies of an unknown distribution f in Rm is presented. These estimators are based on the kth 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.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Uncontrolled Keywords:	Entropy estimation; estimation of statistical distance; estimation of divergence; nearest-neighbor distances; Rényi entropy; Havrda–Charvát entropy; Tsallis entropy
Publisher:	Institute of Mathematical Statistics
ISSN:	0090-5364
Date of First Compliant Deposit:	30 March 2016
Last Modified:	11 May 2023 14:52
URI:	https://orca.cardiff.ac.uk/id/eprint/29550

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