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Exhaustivity, completeness and almost invariance

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Abstract

In this paper, the relationship between exhaustivity (or sufficiency in the sense of Blackwell) and invariance is studied. An analogous result of two classical theorems of Hall, Wijsman and Ghosh (1965) and Berk (1972) on the relationship between sufficiency and invariance is given making use of a concept introduced here under the name of boundedG-completeness; in particular, we get the same conclusion under the assumptions of stability and bounded completeness.

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References

  • Berk, R. (1972). A note on sufficiency and invariance.Annals of Mathematics and Statistics, 39:647–650.

    Google Scholar 

  • Berk, R., Nogales, A., andOyola, J. (1996). Some counterexamples concerning sufficiency and invariance.Annals of Statistics, 24(2):902–905.

    Article  MATH  MathSciNet  Google Scholar 

  • Hall, W., Wijsman, R., andGhosh, J. (1965). The relationship between sufficiency and invariance with applications in sequential analysis.Annals of Mathematics and Statistics, 36:574–614.

    Article  MathSciNet  Google Scholar 

  • Heyer, H. (1982).Theory of Statistical Experiments. Springer Verlag, New York.

    MATH  Google Scholar 

  • Lehmann, E. (1986).Testing Statistical Hypothesis. Wiley, New York.

    Google Scholar 

  • Nogales, A. andOyola, J. (1996). Some remarks on sufficiency, invariance and conditional independence.Annals of Statistics, 24(2):906–909.

    Article  MATH  MathSciNet  Google Scholar 

  • Roy, K. andRamamoorthi, R. (1979). Relationship between Bayes, classical and decision theoretic sufficiency.Sankhyà, Series A, 41(2):48–58.

    MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Departamento de Matemáticas, Universidad de Extremadura, Spain

    J. Montanero, A. Nogales, J. A. Oyola & P. Pérez

Authors
  1. J. Montanero
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  2. A. Nogales
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  3. J. A. Oyola
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  4. P. Pérez
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Corresponding author

Correspondence to A. Nogales.

Additional information

This work was supported by the Junta de Extremadura (Spain) under the project IPR99A016.

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Montanero, J., Nogales, A., Oyola, J.A. et al. Exhaustivity, completeness and almost invariance. Test 11, 405–411 (2002). https://doi.org/10.1007/BF02595714

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  • DOI: https://doi.org/10.1007/BF02595714

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