Nearest neighbor estimates of entropy for multivariate circular distributions

Entropy

Volumn 12, Issue 5, 2010, Pages 1125-1144

  Misra, Neeraj ^a,c   Singh, Harshinder ^a,b   Hnizdo, Vladimir ^b  

^a WEST VIRGINIA UNIVERSITY   (United States)

^b NATIONAL INSTITUTE FOR OCCUPATIONAL SAFETY AND HEALTH   (United States)

^c INDIAN INSTITUTE OF TECHNOLOGY KANPUR   (India)

Author keywords

Circular distance; Circular random variables; Differential entropy; Molecular simulation; Nearest neighbor; Non parametric estimation

Indexed keywords

EID: 77953501154     PISSN: None     EISSN: 10994300     Source Type: Journal    
DOI: 10.3390/e12051125     Document Type: Article

References (23)

1. Karplus, M.; Kushick, J.N. Method for estimating the configurational entropy of macromolecules. Macromolecules 1981, 14, 325-332.
2. Misra, N.; Singh, H.; Demchuk, E. Estimation of the entropy of a multivariate normal distribution. J. Multivar. Anal. 2005, 92, 324-342.
3. Demchuk, E.; Singh, H. Statistical thermodynamics of hindered rotation from computer simulations. Mol. Phys. 2001, 99, 627-636.
4. Singh, H.; Hnizdo, V.; Demchuk, E. Probabilistic modeling of two dependent circular variables. Biometrika 2002, 89, 719-723.
5. Mardia, K.V.; Hughes, G.; Taylor, C.C.; Singh, H. A multivariate von Mises distribution with applications to bioinformatics. Can. J. Stat. 2008, 36, 99-109.
6. Hnizdo, V.; Fedorowicz, A.; Singh, H.; Demchuk, E. Statistical thermodynamics of internal rotation in a hindering potential of mean force obtained from computer simulations. J. Comput. Chem. 2003, 24, 1172-1183.
7. Darian, E.; Hnizdo, V.; Fedorowicz, A.; Singh, H.; Demchuk, E. Estimation of the absolute internal-rotation entropy of molecules with two torsional degrees of freedom from stochastic simulations. J. Comput. Chem. 2005, 26, 651-660.
8. Beirlant, J.; Dudewicz, E.J.; Gyorfi, L.; van der Meulen, E.C. Nonparametric estimation of entropy: An overview. Internat. J. Math. Stat. 1997, 6, 17-39.
9. Scott, D. Multivariate Density Estimation: Theory, Practice and Visualization; Wiley: New York, NY, USA, 1992.
10. Vasicek, O. On a test for normality based on sample entropy. J. R. Stat. Soc. Series B 1976, 38, 54-59.
11. Dudewicz, E.J.; van der Meulen, E.C. Entropy-based tests of uniformity. J. Am. Stat. Assoc. 1981, 76, 967-974.
12. Singh, H.; Misra, N.; Hnizdo, V.; Fedorowicz, E.; Demchuk, E. Nearest neighbor estimates of entropy. Am. J. Math. Manag. Sci. 2003, 23, 301-321.
13. Kozachenko, L.F.; Leonenko, N.N. Sample estimates of entropy of a random vector. Prob. Inf. Trans. 1987, 23, 95-101.
14. Goria, M.N.; Leonenko, N.N.; Novi Inveradi, P.L. A new class of random vector entropy estimators and its applications. Nonparam. Stat. 2005, 17, 277-297.
15. Kraskov, A.; Stögbauer, H.; Grassberger, P. Estimating mutual information. Phys. Rev. E 2004, 69, 066138-1-066138-16.
16. Tsybakov, A.B.; van der Meulen, E.C. Root-n consistent estimators of entropy for densities with unbounded support. Scan. J. Stat. 1996, 23, 75-83.
17. Loftsgaarden, D.O.; Quesenberry, C.P. A non-parametric estimate of a multivariate density function. Ann. Math. Stat. 1965, 36, 1049-1051.
18. n-Nearest neighbor estimators of entropy. Math. Meth. Stat. 2008, 17, 261-277.
19. Lebesgue, H. Sur l'intégration des fonctions discontinues. Ann. Ecole Norm. 1910, 27, 361-450.
20. Hnizdo, V.; Tan, J.; Killian, B.J.; Gilson, M.K. Efficient calculation of configurational entropy from molecular simulations by combining the mutual-information expansion and nearest-neighbor methods. J. Comput. Chem. 2008, 29, 1605-1614.
21. Hnizdo, V.; Darian, E.; Fedorowicz, A.; Demchuk, E.; Li, S.; Singh, H. Nearest-neighbor nonparametric method for estimating the configurational entropy of complex molecules. J. Comput. Chem. 2006, 28, 655-668.
22. Arya, S.; Mount, D.M. Approximate nearest neighbor searching. In the Proceedings of the Fourth Annual ACM-SIAM Symposium on Discrete Algorithms, 25-27 January 1993; p. 271; Available online: http://www.cs.umd.edu/~mount/ANN/ (accessed on 5 May 2010).
23. Friedman, J.H.; Bentley, J.L.; Finkel, R.A. An algorithm for finding best matches in logarithmic expected time. ACM Trans. Math. Software 1977, 3, 209-226.