Estimation of the entropy of a multivariate normal distribution

Journal of Multivariate Analysis

Volumn 92, Issue 2, 2005, Pages 324-342

  Misra, Neeraj ^a,b   Singh, Harshinder ^a,c   Demchuk, Eugene ^a,c  

^a WEST VIRGINIA UNIVERSITY   (United States)

^b INDIAN INSTITUTE OF TECHNOLOGY KANPUR   (India)

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

Author keywords

Affine equivariant estimators; Brewster Zidek type estimator; Entropy; Generalized Bayes estimator; Inadmissible estimator; Quadratic loss function; Risk function; Stein type estimator; Wishart distribution

Indexed keywords

EID: 26644434384     PISSN: 0047259X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmva.2003.10.003     Document Type: Article

References (22)

1. M. Abramowitz A. Stegun Handbook of Mathematical Functions 1965 Dover New York
2. J.F. Brewster J.V. Zidek Improving on equivariant estimators Ann. Statist 2 1974 21-38
3. L.D. Brown On the admissibility of invariant estimators of one or more location parameters Ann. Math. Statist 37 1966 1087-1136
4. N. Go H.A. Scheraga Analysis of the contribution of internal vibrations to the statistical weights of equilibrium conformations of macromolecules J. Chem. Phys 51 1969 4751-4767
5. S.A. Harris E. Gavathiotis M.S. Searle M. Orozco C.A. Laughton Cooperativity in drug-DNA recognition: A molecular dynamics study J. Amer. Chem. Soc 123 50 2001 12658-12663
6. B. Heymann H. Grubmuller Molecular dynamics force probe simulations of antibody/antigen unbinding: Entropic control and nonadditivity of unbinding forces Biophys. J 81 3 2001 1295-1313
7. S. Jusuf P.J. Loll P.H. Axelsen The role of configurational entropy in biochemical cooperativity J. Amer. Chem. Soc 124 14 2002 3490-3491
8. M. Karplus J.N. Kushik Method for estimating the configurational entropy of macromolecules Macromolecules 14 1981 325-332
9. T. Kubokawa Y. Konno Estimating the covariance matrix and the generalized variance under a symmetric loss Ann. Inst. Statist. Math 42 1990 331-343
10. L.D. Landau, E.M. Lifshitz, Statistical Physics, Part 1, 3rd Edition, Butterworth-Heinemann, Oxford, 1980.
11. R.M. Levy M. Karplus J. Kushik D. Perahia Evaluation of the configurational entropy for proteins: Application to molecular dynamics simulations of an α-helix Macromolecules 17 1984 1370-1374
12. R.J. Muirhead Aspects Of Multivariate Statistical Theory 1982 Wiley New York
13. N. Pal Decision-theoretic estimation of generalized variance and generalized precision Comm. Statist. Theor. Methods 17 1988 4221-4230
14. N. Pal Estimation of generalized variance under entropy losses admissibility results Calcutta Statist. Assoc. Bull 38 1989 147-156
15. A.L. Rukhin M.M.A. Ananda Risk behavior of variance estimators in multivariate normal distribution Statist. Probab. Lett 13 1992 159-166
16. H. Schafer L.J. Smith A.E. Mark W.F. van Gunsteren Entropy calculations on the molten goluble state of a protein: Side-chain entropies of alpha-lactalbumin Proteins-Structure Funct. Genet 46 2 2002 215-224
17. R.W. Shorrock J.V. Zidek An improved estimator of the generalized variance Ann. Statist 4 1976 629-638
18. B.K. Sinha On improved estimators of the generalized variance J. Mult. Anal 6 1976 617-625
19. B.K. Sinha M. Ghosh Inadmissibility of the best equivariant estimators of the variance-covariance matrix, the precision matrix and the generalized variance under entropy loss Statist. Decisions 5 1987 201-227
20. C. Stein Inadmissibility of the usual estimator for the variance of a normal distribution with unknown mean Ann. Inst. Statist. Math 16 1964 155-160
21. N. Sugiura Y. Konno Risk of improved estimators of generalized variance and precision in: A.K. Gupta (Ed.), Advances in Multivariate Statistical Analysis 1987 Riedel Holland 353-371
22. S. Xiaoqian P. Wankai Improved estimation of the generalizedprecision under the entropy loss Acta Math. Appl. Sinica 16 2000 162-170