Previous |  Up |  Next


divergence measures; information radius; statistical experiment; sufficiency of experiments; Shannon's entropy; comparison of experiments; stochastic transformations;; unified scalar parametric generalizations of Jensen difference divergence measure
Various information, divergence and distance measures have been used by researchers to compare experiments using classical approaches such as those of Blackwell, Bayesian ets. Blackwell's [1] idea of comparing two statistical experiments is based on the existence of stochastic transformations. Using this idea of Blackwell, as well as the classical bayesian approach, we have compared statistical experiments by considering unified scalar parametric generalizations of Jensen difference divergence measure.
[1] Blackwell D. (1951): Comparison of experiments. Proc. 2nd Berkeley Symp. Berkeley: University of California Press, 93-102. MR 0046002
[2] Burbea J. (1984): The Bose-Einstein Entropy of degree a and its Jensen Difference. Utilitas Math. 25, 225-240. MR 0752861
[3] Burbea J., Rao C . R. (1982): Entropy Differential Metric, Distance and Divergence Measures in Probability Spaces: A Unified Approach. J. Multi. Analy. 12, 575 - 596. DOI 10.1016/0047-259X(82)90065-3 | MR 0680530
[4] Burbea J., Rao C. R. (1982): On the Convexity of some Divergence Measures based on Entropy Functions. IEEE Trans. on Inform. Theory IT-28, 489-495. MR 0672884
[5] Capocelli R. M., Taneja I. J. (1984): Generalized Divergence Measures and Error Bounds. Proc. IEEE Internat. Conf. on Systems, man and Cybernetics, Oct. 9-12, Halifax, Canada, pp. 43 - 47.
[6] Campbell L. L. (1986): An extended Čencov characterization of the Information Metric. Proc. Ann. Math. Soc., 98, 135-141. MR 0848890
[7] Čencov N. N. (1982): Statistical Decisions Rules and Optimal Inference. Trans. of Math. Monographs, 53, Am. Math. Soc., Providence, R. L. MR 0645898
[8] De Groot M. H. (1970): Optimal Statistical Decisions. McGraw-Hill. New York. MR 0356303
[9] Ferentinos K., Papaioannou T. (1982): Information in experiments and sufficiency. J. Statist. Plann. Inference 6, 309-317. DOI 10.1016/0378-3758(82)90001-5 | MR 0667911
[10] Goel P. K., De Groot (1979): Comparison of experiments and information measures. Ann. Statist. 7, 1066-1077. DOI 10.1214/aos/1176344790 | MR 0536509
[11] Kullback S., Leibler A. (1951): On information and sufficiency. Ann. Math Stat. 27, 986-1005.
[12] Lindley D. V. (1956): On a measure of information provided by an experiment. Ann. Math. Statis. 27, 986-1005. DOI 10.1214/aoms/1177728069 | MR 0083936
[13] Marshall A. W., Olkin I. (1979): Inequalities: Theory of Majorization and its Applications. Academic Press. New York. MR 0552278
[14] Morales D., Taneja I. J., Pardo L.: Comparison of Experiments based on $\phi$-Measures of Jensen Difference. Communicated.
[15] Pardo L., Morales D., Taneja I. J.: $\lambda$-measures of hypoentropy and comparison of experiments: Bayesian approach. To appear in Statistica. MR 1173196 | Zbl 0782.62011
[16] Rao C. R. (1982): Diversity and Dissimilarity Coefficients: A Unified Approach. J. Theoret. Pop. Biology, 21, 24-43. DOI 10.1016/0040-5809(82)90004-1 | MR 0662520
[17] Rao C. R., Nayak T. K. (1985): Cross Entropy, Dissimilarity Measures and characterization of Quadratic Entropy. IEEE Trans, on Inform. Theory, IT-31(5), 589-593. DOI 10.1109/TIT.1985.1057082 | MR 0808230
[18] Sakaguchi M. (1964): Information Theory and Decision Making. Unpublished Lecture Notes, Statist. Dept., George Washington Univ., Washington DC.
[19] Sanťanna A. P., Taneja I. J.: Trigonometric Entropies, Jensen Difference Divergence Measures and Error Bounds. Information Sciences 25, 145-156. MR 0794765
[20] Shannon C. E. (1948): A Mathematical Theory of Communications. Bell. Syst. Tech. J. 27, 379-423. MR 0026286
[21] Sibson R. (1969): Information Radius. Z. Wahrs. und verw. Geb. 14, 149-160. MR 0258198
[22] Taneja I. J.: 1(983): On characterization of J-divergence and its generalizations. J. Combin. Inform. System Sci. 8, 206-212. MR 0783757
[23] Taneja I. J. (1986): $\lambda$-measures of hypoentropy and their applications. Statistica, anno XLVI, n. 4, 465-478. MR 0887303
[24] Taneja I. J. (1986): Unified Measure of Information applied to Markov Chains and Sufficiency. J. Comb. Inform. & Syst. Sci., 11, 99-109. MR 0966074
[25] Taneja I. J. (1987): Statistical aspects of Divergence Measures. J. Statist. Plann. & Inferen., 16, 137-145. MR 0895754
[26] Taneja I. J. (1989): On Generalized Information Measures and their Applications. Adv. Elect. Phys. 76, 327 - 413. Academic Press.
[27] Taneja I. J. (1990): Bounds on the Probability of Error in Terms of Generalized Information Radius. Information Sciences. 46.
[28] Taneja I. J., Morales D., Pardo L. (1991): $\lambda$-measures of hypoentropy and comparison of experiments: Blackwell and Lehemann approach. Kybernetika, 27, 413 - 420. MR 1132603
[29] Vajda I. (1968): Bounds on the Minimal Error Probability and checking a finite or countable number of Hypothesis. Inform. Trans. Problems 4, 9-17. MR 0267685
[30] Vajda I. (1989): Theory of Statistical Inference and Information. Kluwer Academic Publishers, Dordrecht/Boston/London/.
Partner of
EuDML logo