Nearest Neighbor Estimates of Entropy for Multivariate Circular Distributions

Entropy

Neeraj Misra¹  Harshinder Singh¹ 

[1] Department of Statistics, West Virginia University, Morgantown, West Virginia 26506, USA

关键词: circular random variables;    differential entropy;    non-parametric estimation;    nearest neighbor;    circular distance;    molecular simulation;   

DOI  :  10.3390/e12051125

来源: mdpi

【 摘 要 】

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 () 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.

【 授权许可】

CC BY   
© 2010 by the authors; licensee MDPI, Basel, Switzerland.