Displaying similar documents to “Some remarks on sufficiency, invariance and conditional independence.”

Statistical models strongly-invariant under the action of a group.

Agustín García Nogales (1990)

Qüestiió

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Some basic results about invariance are given using quotient σ-fields. A strong kind of invariance is considered. Under appropriate conditions we obtain a sufficient statistics for models with such an invariance property.

Two Kinds of Invariance of Full Conditional Probabilities

Alexander R. Pruss (2013)

Bulletin of the Polish Academy of Sciences. Mathematics

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Let G be a group acting on Ω and ℱ a G-invariant algebra of subsets of Ω. A full conditional probability on ℱ is a function P: ℱ × (ℱ∖{∅}) → [0,1] satisfying the obvious axioms (with only finite additivity). It is weakly G-invariant provided that P(gA|gB) = P(A|B) for all g ∈ G and A,B ∈ ℱ, and strongly G-invariant provided that P(gA|B) = P(A|B) whenever g ∈ G and A ∪ gA ⊆ B. Armstrong (1989) claimed that weak and strong invariance are equivalent, but we shall show that this is false...

On the continuity of invariant statistics

Nguyen Van Ho (1978)

Aplikace matematiky

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The aim of this paper is to establish theorems on the absolute continuity of translation as well as scale invariant statistics in general, from which the related results by Hodges-Lehmann and Puri-Sen follow. The continuity relations between the joint cdf of a random vector and its marginal cdf's are also considered.

RUC systems in rearrangement invariant spaces

P. G. Dodds, E. M. Semenov, F. A. Sukochev (2002)

Studia Mathematica

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We present necessary and sufficient conditions for a rearrangement invariant function space to have a complete orthonormal uniformly bounded RUC system.