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Robust slippage tests

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Summary

The robust slippage testing problems ofk+1 approximately known simple hypotheses are formulated as the slippage testing problems ofk+1 composite hypotheses. It is shown that if there is a representativek+1-tuple (called a least favorable slippage tuple) of simple hypotheses, then maximin tests are given by the slippage analogues of the Neyman-Pearson tests for this tuple. Thek-sample case is treated concerning this subject. In the general situations that there does not exist any least favorable slippage tuple, a method for constructing tests is proposed and applied to the case that composite hypotheses are described in terms of certain capacities (ε-contamination, total variation). The variants of the derived tests are also suggested.

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References

  1. Hall, I. J. and Kudô, A. (1968). On slippage tests—(I), A generalization of Neyman-Pearson's lemma,Ann. Math. Statist.,39, 1693–1699.

    Article  MathSciNet  Google Scholar 

  2. Huber, P. J. (1965). Robust version of the probability ratio test,Ann. Math. Statist.,36, 1753–1758.

    Article  MathSciNet  Google Scholar 

  3. Huber, P. J. (1968). Robust confidence limits,Zeit. Wahrscheinlichkeitsth,10, 269–278.

    Article  MathSciNet  Google Scholar 

  4. Huber, P. J. (1981).Robust Statistics, Wiley, New York.

    Book  Google Scholar 

  5. Huber, P. J. and Strassen, V. (1973). Minimax tests and the Neyman-Pearson lemma for capacities,Ann. Statist.,1, 251–263.

    Article  MathSciNet  Google Scholar 

  6. Lehmann, E. L. (1955). Ordered families of distributions,Ann Math. Statist.,26, 399–419.

    Article  MathSciNet  Google Scholar 

  7. Rieder, H. (1977). Least favorable pairs for special capacities,Ann. Statist.,5, 909–921.

    Article  MathSciNet  Google Scholar 

  8. Yao, J. S. and Kudô, A. (1972). On slippage tests—(IV). The invariance of the least favorable distributions,Mem. of the Facu. of Sci. Kyushu Univ., A,26, 323–331.

    MathSciNet  MATH  Google Scholar 

  9. Yeh, N. C. and Kudô, A. (1970). On slippage tests—(III), The least favorable distribution.Tamkang Journal of Mathematics,1, 57–64.

    MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Nanzan University, Nagoya, Japan

    Miyoshi Kimura

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  1. Miyoshi Kimura
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Kimura, M. Robust slippage tests. Ann Inst Stat Math 36, 251–270 (1984). https://doi.org/10.1007/BF02481969

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  • DOI: https://doi.org/10.1007/BF02481969

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