Some properties of a parameterization useful in integrated likelihood inference

Thomas A. Severini ()
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Thomas A. Severini: Northwestern University

Metrika: International Journal for Theoretical and Applied Statistics, 2025, vol. 88, issue 6, No 23, 1327 pages

Abstract: Abstract Consider a model with parameter $$\theta $$ and likelihood function $$L(\theta )$$ . Suppose that $$\theta $$ can be written $$\theta = (\psi, \lambda )$$ , where $$\psi $$ is a real-valued parameter-of-interest and $$\lambda $$ is a nuisance parameter and that our goal is likelihood-based inference regarding $$\psi $$ . In some cases, it may be beneficial to reparameterize the model, keeping the parameter-of-interest unchanged but modifying the nuisance parameter of the model. The purpose of this paper is to present some results regarding a specific nuisance parameter, known as the zero-score expectation (ZSE) parameter, that has been shown to be useful in integrated likelihood inference. These results include a more straightforward motivation for the ZSE parameter, an approximation useful for calculating the corresponding likelihood function, and a new interpretation of an integrated likelihood constructed using the ZSE parameter.

Keywords: Integrated likelihood; Nuisance parameters; Prior distributions; Reparameterization (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00184-025-01006-1

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