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On some sufficient conditions for the existence of a consistent test in noncommutative statistics

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1391)

Keywords

  • Tensor Product
  • Disjoint Subset
  • Spectral Projection
  • Consistent Test
  • Statistical Decision Theory

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References

  1. A. Bartoszewicz, The Projective Limit of Consistent Family of States on Tensor Products of W*-Algebras, Bull. Pol. Acad. Sci. Math. 31, No. 5–8 (1983), 273–279.

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  2. A. Bartoszewicz, Remarks on the Consistency of Tests in Noncommutative Statistics, to appear in Prob. and Math. Stat.

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  3. D. Bures, Tensor product of W*-algebras, Pac. J. Math. 27 (1968), 13–37.

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  4. D. Bures, An extension of Kakutani's theorem on infinite product measures to the tensor product of semifinite W*-algebras, Trans. Amer. Math. Soc. 135 (1969), 199–212.

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  5. A.S. Holevo, The Analogue of Statistical Decision Theory in the Noncommutative Probability Theory, Proc. Moscow Math. Soc. 26 (1972), 133–149.

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  6. H. Kosaki, On the Bures distance and the Uhlmann transition probability of states on a von Neumann algebra, preprint.

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  7. C. Kraft, Some Conditions for Consistency and Uniform Consistency of Statistical Procedures, Univ. Calif. Pub. Stat. 2, No. 6 (1955), 125–141.

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© 1989 Springer-Verlag

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Bartoszewicz, A. (1989). On some sufficient conditions for the existence of a consistent test in noncommutative statistics. In: Cambanis, S., Weron, A. (eds) Probability Theory on Vector Spaces IV. Lecture Notes in Mathematics, vol 1391. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083376

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  • DOI: https://doi.org/10.1007/BFb0083376

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51548-7

  • Online ISBN: 978-3-540-48244-4

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