Nearest neighbor estimates of entropy for multivariate circular distributions
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.
scientific article; zbMATH DE number 5995875