Rényi information, loglikelihood and an intrinsic distribution measure

Journal of Statistical Planning and Inference

Volumn 93, Issue 1-2, 2001, Pages 51-69

  Song, Kai Sheng ^a  

^a FLORIDA STATE UNIVERSITY   (United States)

Author keywords

62A10; 62G20; Heavy tails; Intrinsic shape measure; Kurtosis; Loglikelihood moments; Multivariate t; Primary 62B10; R nyi information; Secondary 62G05; Spectrum; Trigamma function

Indexed keywords

EID: 0041971373     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0378-3758(00)00169-5     Document Type: Article

References (19)

1. Abramowitz M., Stegun I.A. Handbook of Mathematical Functions. 1965;Dover, New York.
2. Ben Bassat M. f -entropies, probability of error, and feature selection Inform. and Control. 39:1978;227-242.
3. Bickel P.J., Lehmann E.L. Descriptive statistics for nonparametric models I. Introduction. Ann. Statist. 3:1975;1038-1044.
4. Cramér H. Mathematical Methods of Statistics. 1946;Princeton University Press, Princeton.
5. Falk M., Hüsler J., Reiss R.-D. Laws of Small Numbers: Extremes and Rare Events. 1994;Birkhäuser, Basel.
6. Good I.J., Gaskins R.A. Nonparametric roughness penalties for probability densities. Biometrika. 58:1971;255-277.
7. Hart P.E. Moment distributions in economics: an exposition. J. Roy. Statist. Soc. Ser. A. 138:1975;423-434.
8. Ibragimov I.A., Has'minskii R.Z. Statistical Estimation. 1981;Springer, New York.
9. Kotz, S., Johnson, N.L., 1985. Encyclopedia of Statistical Sciences. vol. 5, Wiley, New York.
10. Kurths J., Voss A., Saparin P., Witt A., Kleiner H.J., Wessel N. Quantitative analysis of heart rate variability. Chaos. 1:1995;88-94.
11. Mardia K.V. Measures of multivariate skewness and kurtosis with applications. Biometrika. 57:1970;519-530.
12. Morales D., Pardo L., Vajda I. Some new statistics for testing hypotheses in parametric models. J. Multivariate Anal. 62:1997;137-168.
13. Rényi A. On the dimension and entropy of probability distributions. Acta Math. Acad. Sci. Hung. 10:1959;193-215.
14. Rényi A. Az információelmélet néhány alapveto kérdése (Some fundamental problems of the information theory). A Magyar Tudományos Akadémia III Osztályának Közleményei. 10:1960;251-282.
15. Rényi, A., 1961. On measures of entropy and information. Proceedings of the Fourth Berkeley Symposium on Math. Statist. Prob., Vol. I, University of California Press, Berkeley, pp. 547-561.
16. Stute W. A law of the logarithm for kernel density estimators. Ann. Probab. 10:1982;414-422.
17. Vajda I. Bounds of the minimal error probability on checking a finite or countable number of hypotheses. Inform. Transmission Problems. 4:1968;9-17.
18. Vajda I., van der Meulen E.C. Global statistical information in exponential experiments and selection of exponential models. Appl. Math. 43:1998;23-51.
19. van Zwet W.R. Convex Transformations of Random Variables. 1964;Math. Centrum, Amsterdam.