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A generalization of the relative conditional expectatio—Further properties of Pitman'sT * and their applications to statistics

  • Hisataka Kuboki
Article
  • 14 Downloads

Summary

This paper is concerned with the mappingT * which is a generalization of the relative conditional expectation. It has been introduced by E.J.G. Pitman (1979,Some Basic Theory for Statistical Inference, Chapman and Hall).

First we extend the definition of the mappingT * and describe its fundamental properties. Moreover, we establish inequalities for convex functions with respect toT *.

The mappingT * is very useful in analysing quantities associated with the distribution of a statisticT. The application of the mappingT * to statistics is another interest of this paper.

Keywords

Convex Function Integrable Function Fundamental Property Conditional Expectation Finite Measure 
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.

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References

  1. [1]
    Csiszár, I. (1967). Information-type measures of difference of probability distributions and indirect observations,Studia Sci. Math. Hungar.,2, 299–318.MATHMathSciNetGoogle Scholar
  2. [2]
    Inagaki, N. (1983). The decomposition of the Fisher information,Ann. Inst. Statist. Math.,35, 151–165.MATHMathSciNetGoogle Scholar
  3. [3]
    Loève, M. (1977).Probability Theory I, (4th edn.), Springer-Verlag, New York.MATHGoogle Scholar
  4. [4]
    Loève, M. (1978).Probability Theory II, (4th edn.), Springer-Verlag, New York.MATHGoogle Scholar
  5. [5]
    Pitman, E. J. G. (1979).Some Basic Theory for Statistical Inference, Chapman and Hall, London.Google Scholar

Copyright information

© Kluwer Academic Publishers 1984

Authors and Affiliations

  • Hisataka Kuboki

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