On distances and measures of information: A case of diversity

Probability and Statistical Models with Applications

Volumn , Issue , 2000, Pages 503-515

  Papaioannou, Takis ^a  

^a UNIVERSITY OF IOANNINA   (Greece)

Author keywords

Maximum entropy principle; Measure of dependence; Measure of divergence; Measure of information

Indexed keywords

EID: 0346990818     PISSN: None     EISSN: None     Source Type: Book    
DOI: None     Document Type: Chapter

References (40)

1. Aczel, J. (1986). Characterizing information measures: Approaching the end of an era. In Uncertainly in Know ledge-Based Systems. Lecture Notes in Computer Science (Eels., B. Bouchon and R. R. Yager), pp. 359-384. Springer-Verlag, New York.
2. Ah, S. M. and Silvey, S. D. (1966). A general class of coefficients of divergence of one distribution from another. Journal of the Royal Statistical Society, Series B 28, 131-142.
3. Barron, A. and Hengartner, N. (1998). Information theory and super efficiency. Annals of Statistics 26, 1800 1825.
4. Csiszar, I. (1977). Information measures: A critical review. Transactions of the 7th Prague Conference on Informa, lion Theory, Statistical Decision Functions and Random Processes, pp. 73-86, Prague, 1974, Academia.
5. Cutler, A. and Cordero-Brana, O. I. (1996). Minimun Hellinger distance estimation for finite mixture models. Journal of the American Statistical Association 91, 1716-1723.
6. Ebrahimi, N. and Soofi, E. S. (1990). Relative information loss under Type II censored experimental data. Biometrika 77, 429-435
7. Ferentinos, K. and Papaioannou, T. (1981). New parametric measures of information. Information and Control 51, 193-208.
8. Guiasu, S. arid Reischer, C. (1985). The relative information generating function. Information and Sciences 35, 235-241.
9. Hartigan, J. A. (1998). The maximum likelihood prior. Annals of Statistics 26, 2083-2103.
10. Hollander, M., Proschan, F., and Sconing, J. (1987). Measuring information in the right-censored models. Naval Research Logistics34, 669-687.
11. Jensen, U. (1993). Derivation and calculation of Rao distances: a review. Technical Report 71/1993. Institut fur Statistik und Ökonometrie der Universität Kiel.
12. Kagan, A. and Landsman, Z. (1997). Statistical meaning of Carlen’s superadditivity of the Fisher information. Statistics & Probability Letters 32, 175-179.
13. Kateri, M. and Papaioannou, T. (1994). f-divergence association models. International Journal of Mathematical and Statistical Sciences 3, 179-203.
14. Kateri, M. and Papaioannou, T. (1997). Symmetry and asymmetry models for rectangular contingency tables. Journal of the American Statistical Association 92, 1124-1131.
15. Kendall, M. G. (1973). Entropy, probability and information. International Statistical Review 41, 59-68.
16. Kuliback, S. (1959). Information Theory and Statistics. John Wiley & Sons, New York.
17. Kuppcrrnan, M. (1957). Further Applications of Information Theory to Multivariate Analysis and Statistical Inference. Ph.D. dissertation, George Washington University, Washington, D.C.
18. Lindley, D. V. (1956). On a measure of the information provided by an experiment. Annals of Mathematical Statistics 27, 986-1005.
19. Morales, D., Pardo, L., Salicru, M., and Menendez, M. L. (1993). The A-divcrgence and the A-mutual information: Estimation in stratified sampling. Journal of Computational and Applied Mathematics 47, 1-10.
20. Morales, D., Pardo, L., Salicru, M., and Menendez, M. L. (1994). Asymptotic properties of divergence statistics in stratified random sampling and its application to test statistical hypotheses. Journal of Statistical Planning and Inference 38, 201-223.
21. Morales, D., Pardo, L., and Vajda, I. (1995). Asymptotic divergence of estimates of discrete distributions. Journal of Statistical Planning inference 48, 347-369.
22. Nayak, T. K. (1985). On diversity measures based on entropy functions. Communications in Statistics — Theory and Methods14, 203-215.
23. Papaioannou, T. (1971). A criterion of estimation based on measures of information, Unpublished manuscript, University of Georgia. Abstract, Annals of Mathematical Statistics42, 2179.
24. Papaioannou, T. (1985). Measures of information. In Encyclopedia of Statistical Sciences 5 (Eds., S. Kotz and N. L. Johnson), pp. 391-397. John Wiley & Sons, New York.
25. Papaioannou, T. and Kcmpthornc, O. (1971). On Statistical Information Theory and Related Measures of Information. Technical Report No. ARL. 71-0059, Aerospace Research Laboratories, Wright-Patterson A.F.B., Ohio.
26. Papathanasiou, V. (1993). Some characteristic properties of the Fisher information matrix via Cacoullos-type inequalities. Journal of Multivariate Analysis, 44, 256-265.
27. Pardo, L. (1999). Generalized divergence measures: statistical applications. In Encyclopedia of Microcomputers, pp. 163-191. Marcel-Dekker, New York.
28. Pardo, L., Morales, D., Salicru, M., and Menendcz, M. L. (1993). The α-divergencc statistic in bivariate multinomial populations including stratification. Metrika 40, 223-235.
29. Pardo, L., Salicru, M., Menendcz, M. L., and Morales, D. (1995). A test for homogeneity of variances based on Shannonss entropy. Metron 53, 135-146.
30. Pardo, L. and Taneja, I.J. (1991). Information energy and its applications. Advances in Electronics and Electron Physics 90, 165-241.
31. Read, T. R. C. and Cressie, N. A. C. (1988). Goodness-up-Pit Statistics for Discrete Multivariate Data. Springer-Verlag, New York.
32. Salicru, M., Morales, D., Menendcz, M. L., and Pardo, L. (1994). On the applications of divergence type measures in testing statistical hypotheses. Journal of Multivariate Analysis 51, 372-391.
33. Soofi, E. S. (1994). Capturing the intangible concept of information. Journal of the American Statistical Association 89, 1243-1254.
34. Taneja, I. J. (1989). On generalized information measures and their applications. Advances in Electronics and Electron Physics76, 327-413.
35. Thclen, B. J. (1989). Fisher information and dichotomies in equiv-alence/contiguity. Annals of Statistics 17, 1664-1690.
36. Tsairidis, Ch., Ferentinos, K., and Papaioannou, T. (1996). Information and random censoring. Information Sciences 92, 159-174.
37. Tsairidis, Ch., Zografos, K., Ferentinos, K., and Papaioannou, T. (2000). Information in quantal response data and random censoring. Annals of the Institute of Statistical Mathematics (to appear).
38. Zografos, K. (1993). Asymptotic properties of ^divergence statistic and its applications in contingency tables. International Journal of Mathematical and Statistical Sciences 2, 5-21.
39. Zografos, K. (1998). f-dissimilarity of several distributions in testing statistical hypotheses. Annals of the Institute of Statistical Mathematics 50, 295-310.
40. Zografos, K., Ferentinos, K., and Papaioannou, T. (1990). φ-diverg-ence statistics: sampling properties and multinomial goodness of fit and divergence tests. Communications in Statistics — -Theory and Methods 19, 1785-1802.