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Some Information Theoretic Ideas Useful in Statistical Inference

Author

Listed:
  • Takis Papaioannou

    (University of Piraeus)

  • Kosmas Ferentinos

    (University of Ioannina)

  • Charalampos Tsairidis

    (Democritus University of Thrace)

Abstract

In this paper we discuss four information theoretic ideas and present their implications to statistical inference: (1) Fisher information and divergence generating functions, (2) information optimum unbiased estimators, (3) information content of various statistics, (4) characterizations based on Fisher information.

Suggested Citation

  • Takis Papaioannou & Kosmas Ferentinos & Charalampos Tsairidis, 2007. "Some Information Theoretic Ideas Useful in Statistical Inference," Methodology and Computing in Applied Probability, Springer, vol. 9(2), pages 307-323, June.
    • Handle: RePEc:spr:metcap:v:9:y:2007:i:2:d:10.1007_s11009-007-9017-7
    DOI: 10.1007/s11009-007-9017-7
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    References listed on IDEAS

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    3. Papathanasiou, V., 1993. "Some Characteristic Properties of the Fisher Information Matrix via Cacoullos-Type Inequalities," Journal of Multivariate Analysis, Elsevier, vol. 44(2), pages 256-265, February.
    4. Zheng, Gang, 2001. "A characterization of the factorization of hazard function by the Fisher information under Type II censoring with application to the Weibull family," Statistics & Probability Letters, Elsevier, vol. 52(3), pages 249-253, April.
    5. Rothenberg, Thomas J, 1971. "Identification in Parametric Models," Econometrica, Econometric Society, vol. 39(3), pages 577-591, May.
    6. Z. Abo-Eleneen & H. Nagaraja, 2002. "Fisher Information in an Order Statistic and its Concomitant," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(3), pages 667-680, September.
    7. Gertsbakh, Ilya & Kagan, Abram, 1999. "Characterization of the Weibull distribution by properties of the Fisher information under type-I censoring," Statistics & Probability Letters, Elsevier, vol. 42(1), pages 99-105, March.
    8. Paul Vos, 1992. "Minimum f-divergence estimators and quasi-likelihood functions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 44(2), pages 261-279, June.
    9. Konstantinos Zografos & Kosmas Ferentinos, 1994. "An information theoretic argument for the validity of the exponential model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 41(1), pages 109-119, December.
    10. Ch. Tsairidis & K. Zografos & K. Ferentinos & T. Papaioannou, 2001. "Information in Quantal Response Data and Random Censoring," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(3), pages 528-542, September.
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