-information radius of type and comparison of experiments

Inder Jeet Taneja; Luis Pardo; D. Morales

Applications of Mathematics (1991)

  • Volume: 36, Issue: 6, page 440-455
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Taneja, Inder Jeet, Pardo, Luis, and Morales, D.. "$(R,S)$-information radius of type $t$ and comparison of experiments." Applications of Mathematics 36.6 (1991): 440-455. <http://eudml.org/doc/15692>.

@article{Taneja1991,
abstract = {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.},
author = {Taneja, Inder Jeet, Pardo, Luis, Morales, D.},
journal = {Applications of Mathematics},
keywords = {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; comparison of experiments; stochastic transformations; unified scalar parametric generalizations of Jensen difference divergence measure; information radius; sufficiency of experiments; Shannon's entropy},
language = {eng},
number = {6},
pages = {440-455},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {$(R,S)$-information radius of type $t$ and comparison of experiments},
url = {http://eudml.org/doc/15692},
volume = {36},
year = {1991},
}

TY - JOUR
AU - Taneja, Inder Jeet
AU - Pardo, Luis
AU - Morales, D.
TI - $(R,S)$-information radius of type $t$ and comparison of experiments
JO - Applications of Mathematics
PY - 1991
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 36
IS - 6
SP - 440
EP - 455
AB - 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.
LA - eng
KW - 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; comparison of experiments; stochastic transformations; unified scalar parametric generalizations of Jensen difference divergence measure; information radius; sufficiency of experiments; Shannon's entropy
UR - http://eudml.org/doc/15692
ER -

References

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  1. Blackwell D. (1951), Comparison of experiments, Proc. 2nd Berkeley Symp. Berkeley: University of California Press, 93-102. MR0046002
  2. Burbea J. (1984), The Bose-Einstein Entropy of degree a and its Jensen Difference, Utilitas Math. 25, 225-240. MR0752861
  3. Burbea J., Rao C . R. (1982), 10.1016/0047-259X(82)90065-3, J. Multi. Analy. 12, 575 - 596. MR0680530DOI10.1016/0047-259X(82)90065-3
  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. MR0672884
  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. MR0848890
  7. Čencov N. N. (1982), Statistical Decisions Rules and Optimal Inference, Trans. of Math. Monographs, 53, Am. Math. Soc., Providence, R. L. MR0645898
  8. De Groot M. H. (1970), Optimal Statistical Decisions, McGraw-Hill. New York. MR0356303
  9. Ferentinos K., Papaioannou T. (1982), 10.1016/0378-3758(82)90001-5, J. Statist. Plann. Inference 6, 309-317. MR0667911DOI10.1016/0378-3758(82)90001-5
  10. Goel P. K., De Groot (1979), 10.1214/aos/1176344790, Ann. Statist. 7, 1066-1077. MR0536509DOI10.1214/aos/1176344790
  11. Kullback S., Leibler A. (1951), On information and sufficiency, Ann. Math Stat. 27, 986-1005. 
  12. Lindley D. V. (1956), 10.1214/aoms/1177728069, Ann. Math. Statis. 27, 986-1005. MR0083936DOI10.1214/aoms/1177728069
  13. Marshall A. W., Olkin I. (1979), Inequalities: Theory of Majorization and its Applications, Academic Press. New York. MR0552278
  14. Morales D., Taneja I. J., Pardo L., Comparison of Experiments based on -Measures of Jensen Difference, Communicated. 
  15. Pardo L., Morales D., Taneja I. J., -measures of hypoentropy and comparison of experiments: Bayesian approach, To appear in Statistica. Zbl0782.62011MR1173196
  16. Rao C. R. (1982), 10.1016/0040-5809(82)90004-1, J. Theoret. Pop. Biology, 21, 24-43. MR0662520DOI10.1016/0040-5809(82)90004-1
  17. Rao C. R., Nayak T. K. (1985), 10.1109/TIT.1985.1057082, IEEE Trans, on Inform. Theory, IT-31(5), 589-593. MR0808230DOI10.1109/TIT.1985.1057082
  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. MR0794765
  20. Shannon C. E. (1948), 10.1002/j.1538-7305.1948.tb01338.x, Bell. Syst. Tech. J. 27, 379-423. MR0026286DOI10.1002/j.1538-7305.1948.tb01338.x
  21. Sibson R. (1969), 10.1007/BF00537520, Z. Wahrs. und verw. Geb. 14, 149-160. MR0258198DOI10.1007/BF00537520
  22. Taneja I. J.: 1(983), On characterization of J-divergence and its generalizations, J. Combin. Inform. System Sci. 8, 206-212. MR0783757
  23. Taneja I. J. (1986), -measures of hypoentropy and their applications, Statistica, anno XLVI, n. 4, 465-478. MR0887303
  24. Taneja I. J. (1986), Unified Measure of Information applied to Markov Chains and Sufficiency, J. Comb. Inform. & Syst. Sci., 11, 99-109. MR0966074
  25. Taneja I. J. (1987), 10.1016/0378-3758(87)90063-2, J. Statist. Plann. & Inferen., 16, 137-145. MR0895754DOI10.1016/0378-3758(87)90063-2
  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), -measures of hypoentropy and comparison of experiments: Blackwell and Lehemann approach, Kybernetika, 27, 413 - 420. MR1132603
  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. MR0267685
  30. Vajda I. (1989), Theory of Statistical Inference and Information, Kluwer Academic Publishers, Dordrecht/Boston/London/. 

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