Application of an adequate statistic to the invariant prediction region

  • Yoshikazu Takada


Multivariate Normal Distribution Adequate Statistic Prediction Region Lower Triangular Matrice Conditional Density Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Basu, D. (1955). On statistics independent of a complete sufficient statistics,Sankhyā,15, 377–380.MATHGoogle Scholar
  2. [2]
    Epstein, B. and Sobel, M. (1954). Some theorems relevant to life testing from an exponential distribution,Ann. Math. Statist.,25, 373–381.MATHMathSciNetGoogle Scholar
  3. [3]
    Fraser, D. A. S. (1968).The Structure of Inference, Wiley, New York.MATHGoogle Scholar
  4. [4]
    Giri, N. C. (1977).Multivariate Statistical Inference, Academic Press, New York.MATHGoogle Scholar
  5. [5]
    Hall, W. J., Wijsman, R. A. and Ghosh, J. K. (1965). The relationship between sufficiency and invariance with application in sequential analysis,Ann. Math. Statist.,36, 575–614.MATHMathSciNetGoogle Scholar
  6. [6]
    Halmos, P. R. and Savage, L. J. (1949). Application of Radon-Nikodym theorem to the theory of sufficient statistics,Ann. Math. Statist.,20, 225–241.MATHMathSciNetGoogle Scholar
  7. [7]
    Ishii, G. (1980). Best invariant prediction region based on an adequate statistic,Recent Development in Statistical Inference and the Data Analysis (ed. K. Matusita), North-Holland.Google Scholar
  8. [8]
    Lehmann, E. L. (1953).Testing Statistical Hypotheses, Wiley, New York.Google Scholar
  9. [9]
    Likěs, J. (1974). Prediction ofsth ordered observation for the two-parameter exponential distribution,Technometrics,16, 241–244.MathSciNetCrossRefGoogle Scholar
  10. [10]
    Skibinsky, M. (1967). Adequate subfields and sufficiency,Ann. Math. Statist.,38, 155–161.MATHMathSciNetGoogle Scholar
  11. [11]
    Sugiura, M. and Morimoto, H. (1969). Factorization theorem for adequate σ-field,Sūgaku,21, 286–289 (in Japanese).Google Scholar
  12. [12]
    Takada, Y. (1979). The shortest invariant prediction interval from the largest observation from the exponential distribution,J. Japan Statist. Soc.,9, 87–91.MathSciNetGoogle Scholar
  13. [13]
    Takada, Y. (1981). Invariant prediction rules and an adequate statistic,Ann. Inst. Statist. Math.,33, A, 91–100.MATHMathSciNetGoogle Scholar
  14. [14]
    Takeuchi, K. (1975).Statistical Prediction Theory, Baihūkan, Tokyō (in Japanese).Google Scholar
  15. [15]
    Takeuchi, K. and Akahira, M. (1975). Characterizations of prediction sufficiency (adequacy) in terms of risk function.Ann. Statist.,3, 1018–1024.MATHMathSciNetGoogle Scholar

Copyright information

© Kluwer Academic Publishers 1982

Authors and Affiliations

  • Yoshikazu Takada
    • 1
  1. 1.Kumamoto UniversityKumamotoJapan

Personalised recommendations