Minimal Suuciency of Order Statistics in Convex Models
نویسنده
چکیده
Let P be a convex and dominated statistical model on the measurable space (X ; A), with A minimal suucient, and let n 2 N. Then A n sym , the-algebra of all permutation invariant sets belonging to the n-fold product-algebra A n , is shown to be minimal suucient for the corresponding model for n independent observations, P n = fP n : P 2 Pg. The main technical tool provided and used is a functional analogue of a theorem of Grzegorek (1982) concerning generators of A n sym .
منابع مشابه
Minimal sufficiency of order statistics in convex models
Let P be a convex and dominated statistical model on the measurable space (X ,A), with A minimal sufficient, and let n ∈ N. Then A⊗n sym, the σ-algebra of all permutation invariant sets belonging to the n-fold product σ-algebra A⊗n, is shown to be minimal sufficient for the corresponding model for n independent observations, Pn = {P⊗n : P ∈ P}. The main technical tool provided and used is a fun...
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