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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 functional analogue of a theorem of Grzegorek (1982) concerning generators of A⊗n sym.

Minimal sufficiency of order statistics in convex models