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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Minimal sufficiency of order statistics in convex models
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by Lutz Mattner PDF
Proc. Amer. Math. Soc. 129 (2001), 3401-3411 Request permission

Abstract:

Let $\mathcal {P}$ be a convex and dominated statistical model on the measurable space $(\mathcal {X},\mathcal {A})$, with $\mathcal {A}$ minimal sufficient, and let $n\in \mathbb {N}$. Then $\mathcal {A}^{\otimes n}_{\operatorname {sym}}$, the $\sigma$-algebra of all permutation invariant sets belonging to the $n$-fold product $\sigma$-algebra $\mathcal {A}^{\otimes n}$, is shown to be minimal sufficient for the corresponding model for $n$ independent observations, $\mathcal {P}^n = \left \{P^{\otimes n}:P\in \mathcal {P}\right \}$. The main technical tool provided and used is a functional analogue of a theorem of Grzegorek (1982) concerning generators of $\mathcal {A}^{\otimes n}_{\operatorname {sym}}$.
References
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Additional Information
  • Lutz Mattner
  • Affiliation: Department of Statistics, University of Leeds, Leeds LS2 9JT, United Kingdom
  • MR Author ID: 315405
  • Email: mattner@amsta.leeds.ac.uk
  • Received by editor(s): November 13, 1999
  • Received by editor(s) in revised form: March 30, 2000
  • Published electronically: May 10, 2001
  • Communicated by: Wei Y. Loh
  • © Copyright 2001 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 129 (2001), 3401-3411
  • MSC (2000): Primary 62B05, 62G30, 28A35
  • DOI: https://doi.org/10.1090/S0002-9939-01-06006-3
  • MathSciNet review: 1845019