Statistical estimation of quadratic Rényi entropy for a stationary m-dependent sequence

Källberg, David, Leonenko, Nikolai N. ORCID: https://orcid.org/0000-0003-1932-4091 and Seleznjev, Oleg 2014. Statistical estimation of quadratic Rényi entropy for a stationary m-dependent sequence. Journal of Nonparametric Statistics 26 (2) , pp. 385-411. 10.1080/10485252.2013.854438

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Abstract

The Rényi entropy is a generalisation of the Shannon entropy and is widely used in mathematical statistics and applied sciences for quantifying the uncertainty in a probability distribution. We consider estimation of the quadratic Rényi entropy and related functionals for the marginal distribution of a stationary m-dependent sequence. The U-statistic estimators under study are based on the number of ε-close vector observations in the corresponding sample. A variety of asymptotic properties for these estimators are obtained (e.g. consistency, asymptotic normality, and Poisson convergence). The results can be used in diverse statistical and computer science problems whenever the conventional independence assumption is too strong (e.g. ε-keys in time series databases and distribution identification problems for dependent samples).

Item Type:	Article
Date Type:	Published Online
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Uncontrolled Keywords:	entropy estimation, quadratic Rényi entropy, stationary m\-dependent sequence, U\-statistics, inter\-point distances
Publisher:	Taylor & Francis
ISSN:	1048-5252
Date of Acceptance:	5 October 2013
Last Modified:	25 Oct 2022 09:33
URI:	https://orca.cardiff.ac.uk/id/eprint/59091

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