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Eliminating nuisance parameters: two characterizations

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Abstract

Given a statistical modelP = {Pθ : θ ∈ x} and a surjective functiong: ϑ→Λ the problem of transformingP into a new modelQ= {λ : λ ∈ Λ} indexed by Λ is investigated. Two characterizations are given for those modelsQ of the form Qλ = ∫ Pθ πλ(dθ), where πλ is some probability such that πλ(g=λ)=1. The first is related to a geometric property ofQ, while the second rests on the inferential implications of adoptingQ. 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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Authors and Affiliations

  1. Dipartimento di Metodi Quantitativi, Università di Siena, Italy

    Lorenzo Fattorini

  2. Dipartimento di Statistica “G. Parenti”, Università di Firenze, Italy

    Pietro Rigo

  3. Dipartimento di Matematica Pura ed Applicata “G. Vitali”, Università di Modena, Via Campi 213, B-41100, Modena, Italy

    Patrizia Berti

Authors
  1. Patrizia Berti
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  2. Lorenzo Fattorini
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  3. Pietro Rigo
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Correspondence to Patrizia Berti.

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Berti, P., Fattorini, L. & Rigo, P. Eliminating nuisance parameters: two characterizations. Test 9, 133–148 (2000). https://doi.org/10.1007/BF02595855

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  • DOI: https://doi.org/10.1007/BF02595855

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