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Uniform θ-equivalence of probability distributions based on information and related measures of discrepancy

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Summary

Some criteria based on K-L information number andW-divergence are presented for a certain type of uniform approximate equivalence of two probability distributions. As applications, some necessary and sufficient conditions are also given for the corresponding uniform asymptotic equivalence of two random sequences.

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References

  1. Ikeda, S. (1963). Asymptotic equivalence of probability distributions to some problems of asymptotic independence,Ann. Inst. Statist. Math.,15, 87–116.

    Article  MathSciNet  Google Scholar 

  2. Ikeda, S. (1968). Asymptotic equivalence of real probability distributions,Ann. Inst. Statist. Math.,20, 339–362.

    Article  MathSciNet  Google Scholar 

  3. Ikeda, S. and Matsunawa, T. (1972). On the uniform asymptotic joint normality of sample quantiles,Ann. Inst. Statist. Math.,24, 33–52.

    Article  MathSciNet  Google Scholar 

  4. Kagan, A. M. (1963). On the theory of Fisher's amount of information,Dokl. Akad. Nauk, SSSR,151, 277–278.

    MathSciNet  MATH  Google Scholar 

  5. Matsunawa, T. (1976). Some inequalities based on inverse factorial series,Ann. Inst. Statist. Math.,28, A, 291–305.

    Article  MathSciNet  Google Scholar 

  6. Matsunawa, T. (1977). Approximations to the probabilities of binomial and multinomial random variables and chi-square type statistics,Ann. Inst. Statist. Math.,29, A, 333–358.

    Article  MathSciNet  Google Scholar 

  7. Pinsker, M. S. (1964).Information and Information Stability of Random Variables and Processes, Holden-Day, Inc.

  8. Rényi, A. (1970).Foundations of Probability, Holden-Day, Inc.

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Authors
  1. T. Matsunawa
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The Institute of Statistical Mathematics

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Matsunawa, T. Uniform θ-equivalence of probability distributions based on information and related measures of discrepancy. Ann Inst Stat Math 34, 1–17 (1982). https://doi.org/10.1007/BF02481004

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  • DOI: https://doi.org/10.1007/BF02481004

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