Partial Sufficiency with Connection to the Identification Problem

Oulhaj, Abderrahim;Mouchart, Michel
(2003) Metron : international journal of statistics — Vol. 61, n° 2, p. 267-283 (2003)

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  • Oulhaj, AbderrahimUCLouvain
    Author
  • Mouchart, MichelUCLouvain
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Abstract
Let MΘX = (RX , X , PΘ = {pθ : θ ∈Θ})be a parametrized statistical model and g : Θ→ G be a non-injective function characterizing a parameter of interest. The basic idea of partial sufficiency is to find a (minimal) statistic sufficient for making inference on g(θ). Following Fraser (1956), Barndorff-Nielsen (1978) has defined a concept of S-sufficiency. Our contribution is first to establish the connection between S-sufficiency and the identification concept. Second, we establish some properties of S-sufficiency, in particular we compare the properties of sufficiency for the complete parameter with those of S-sufficiency.
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Oulhaj, A., & Mouchart, M. (2003). Partial Sufficiency with Connection to the Identification Problem. Metron : international journal of statistics, 61(2), 267-283. (Original work published 2003)