Nearest neighbor estimates of entropy for multivariate circular distributions
type: Item
instance of: scholarly article
title: Nearest neighbor estimates of entropy for multivariate circular distributions
zbMATH Open document ID: 1229.62037
author: Neeraj Misra
author: Harshinder Singh
author: Vladimir Hnizdo
published in: Entropy
publication date: 2012-01-09T00:00:00Z
review text: Summary: In molecular sciences, the estimation of entropies of molecules is important for the understanding of many chemical and biological processes. Motivated by these applications, we consider the problem of estimating the entropies of circular random vectors and introduce nonparametric estimators based on circular distances between \(n\) sample points and their \(k\)-th nearest neighbors (NN), where \(k\, (\leq n-1)\) is a fixed positive integer. The proposed NN estimators are based on two different circular distances, and are asymptotically unbiased and consistent. The performance of one of the circular-distance estimators is compared with that of the already established Euclidean-distance NN estimator using Monte Carlo samples from an analytic distribution of six circular variables of an exactly known entropy and a large sample of seven internal-rotation angles in the molecule of tartaric acid, obtained by a realistic molecular-dynamics simulation.
Mathematics Subject Classification ID: 62G05
Mathematics Subject Classification ID: 62B10
Mathematics Subject Classification ID: 92C40
Mathematics Subject Classification ID: 62H11
Mathematics Subject Classification ID: 65C05
zbMATH DE Number: 5995875
zbMATH Keywords: circular random variables
zbMATH Keywords: differential entropy
zbMATH Keywords: non-parametric estimation
zbMATH Keywords: nearest neighbor
zbMATH Keywords: circular distance
zbMATH Keywords: molecular simulation
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3390/e12051125
OpenAlex ID: W2071875548
Wikidata QID: Q23918836
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DOI: 10.3390/E12051125
description: scientific article; zbMATH DE number 5995875