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On the theory of statistical decision functions

  • Kameo Matusita
Article

Keywords

Compact Space Decision Function Arbitrary Positive Number Unifo Minimax Solution 

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References

  1. 1).
    Cf. J. Ville’s note “Sur la théorie générale des jeúc oú intervient l’habilité des joucurs” in E. Borel “Traitédu calcul des probabilités et de ses applications, Tome TV, Facsc. II.”Google Scholar
  2. 2).
    As to this theorem cf. also S. Kakutani,On Equivalence of Infinite Product Measure, Ann. Math. vol. 49 (1948).Google Scholar
  3. 3).
    As to this theorem cf. also R. von Mises,On the Problem of Testing Hypotheses, Ann. Math. Stat. vol. 14 (1943) and H. Kudo,On the “Power” Functions, Research Memoirs of the Institute of Statistical Mathematics vol. 4 (1948) (in Japanese)Google Scholar
  4. 4).
    cf. the Addendum below.Google Scholar
  5. 5).
    As to this Addendum cf. A. Dvoretzky, A. Wald and J. Wolfowitz,Elimination in Certain Statistical Decision Procedures and Zero-Sum Two-Person Games, Ann. Math. Stat. Vol. 22 (1951).Google Scholar
  6. 6).
    A. Dvoretzky, A. Wald and J. Wolfowitz,Relations among certain Ranges of Vector Measures, Lemma 2, Pacific J. Math. Vol. I.Google Scholar

Copyright information

© The Institute of Statistical Mathematics, Tokyo 1951

Authors and Affiliations

  • Kameo Matusita
    • 1
  1. 1.Institute of Statistical MathematicsJapan

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