Given a statistical model P = {Pθ : θ ∈ Θ} and a surjective function g : Θ → Λ, the problem of transforming P into a new model Q = {Qλ : λ ∈ Λ} indexed by Λ is investigated. Two characterizations are given for those models Q of the form Qλ = ∫Pθπλ(dθ), where πλ is some probability such that πλ(g = λ) = 1. The first is related to a geometric property of Q, while the second rests on the inferential implications of adopting Q. Also, in the first πλ is allowed to be finitely additive, while in the second πλ is σ-additive. Finally, integrated likelihoods are revisited in light of the second characterization.
Berti, P., Fattorini, L., Rigo, P. (2000). Eliminating nuisance parameters: two characterizations. TEST, 9(1), 133-148 [10.1007/BF02595855].
Eliminating nuisance parameters: two characterizations
Fattorini, Lorenzo;
2000-01-01
Abstract
Given a statistical model P = {Pθ : θ ∈ Θ} and a surjective function g : Θ → Λ, the problem of transforming P into a new model Q = {Qλ : λ ∈ Λ} indexed by Λ is investigated. Two characterizations are given for those models Q of the form Qλ = ∫Pθπλ(dθ), where πλ is some probability such that πλ(g = λ) = 1. The first is related to a geometric property of Q, while the second rests on the inferential implications of adopting Q. Also, in the first πλ is allowed to be finitely additive, while in the second πλ is σ-additive. Finally, integrated likelihoods are revisited in light of the second characterization.
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https://hdl.handle.net/11365/22297
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