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Nearest Neighbor Estimates of Entropy for Multivariate Circular Distributions
Department of Statistics, West Virginia University, Morgantown, West Virginia 26506, USA
National Institute for Occupational Safety and Health, Morgantown, West Virginia 26505, USA
Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, Kanpur 208 016, India
* Author to whom correspondence should be addressed.
Received: 26 February 2010 / Accepted: 29 April 2010 / Published: 6 May 2010
Abstract: 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 non-parametric estimators based on circular distances between n sample points and their k th nearest neighbors (NN), where k (≤ n – 1) is a fixed positive integer. The proposed NN estimators are based on two different circular distances, and are proven to be asymptotically unbiased and consistent. The performance of one of the circular-distance estimators is investigated and 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.
Keywords: circular random variables; differential entropy; non-parametric estimation; nearest neighbor; circular distance; molecular simulation
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MDPI and ACS Style
Misra, N.; Singh, H.; Hnizdo, V. Nearest Neighbor Estimates of Entropy for Multivariate Circular Distributions. Entropy 2010, 12, 1125-1144.
Misra N, Singh H, Hnizdo V. Nearest Neighbor Estimates of Entropy for Multivariate Circular Distributions. Entropy. 2010; 12(5):1125-1144.
Misra, Neeraj; Singh, Harshinder; Hnizdo, Vladimir. 2010. "Nearest Neighbor Estimates of Entropy for Multivariate Circular Distributions." Entropy 12, no. 5: 1125-1144.