Integrated likelihood functions for non-Bayesian inference

Severini, Thomas A.

doi:10.1093/biomet/asm040

Cited by 43 publications

(54 citation statements)

References 21 publications

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“…In particular, there are asymptotic connections between adjustments of the profile likelihood and refinements of the estimative predictive density. These connections provide a new rationale for modifications of the profile likelihood, that complements the results in Severini (1998aSeverini ( , 2007 and in Pace and Salvan (2006). Moreover, the result suggests how to construct adjusted profile likelihoods using accurate predictive densities.…”

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confidence: 61%

Adjustments of profile likelihood through predictive densities

2010

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confidence: 61%

Adjustments of profile likelihood through predictive densities

2010

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“…For instance, this has lead to the investigation of integrated likelihood functions for non-Bayesian inference (Liseo, 1993, Berger et al, 1999, Severini, 2007, 2010, 2011, to the development of matching priors that ensure approximate frequentist validity of posterior credible regions (see e.g. Datta and Mukerjee, 2004), to the use Bayesian expansions for frequentist computations (see, for instance, Mukerjee and Reid, 2000), and to the use of pseudo-likelihood functions for Bayesian inference (see, among others, Severini, 1999 In particular, the agreement between the frequentist and posterior coverage probabilities of credible regions, arising from matching priors on ψ only derived from L mp (ψ), provides a validation for these priors, and hence their study is of interest from the frequentist viewpoint as well.…”

Section: Background Theorymentioning

confidence: 99%

On interval and point estimators based on a penalization of the modified profile likelihood

Ventura

Racugno

2012

Statistics & Probability Letters

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Various modifications of the profile likelihood have been proposed in the literature. Despite modified profile likelihood methods have better properties than those based on the profile likelihood, the signed likelihood ratio statistic based on the modified profile likelihood has a standard normal distribution only to first order, and it can be inaccurate in particular in models with many nuisance parameters. In this paper we propose an adjustment of the profile likelihood from a new perspective. The idea is to resort to suitable default priors on the parameter of interest only to be used as non-negative weight functions in order to modify the modified profile likelihood. In particular, we focus on matching priors, i.e. priors on the parameter of interest only for which there is an agreement between frequentist and Bayesian inference, derived from modified profile likelihoods. The proposed modified profile likelihood has desiderable inferential properties: the corresponding signed likelihood ratio statistic is standard normal to second order and the correponding maximizer is a refinement of the maximum likelihood estimator, which improves its small sample properties. Examples illustrate the proposed modified profile likelihood and outline its improvement over its counterparts.

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“…This mimics the "integrated likelihood" approach discussed by Severini (2007) and Lehmann (2006). Though the idea of local likelihood for GLMs has been around for some time (Hastie and Tibshirani, 1987;Loader, 1999), to our knowledge, we are not aware of using the integrated likelihood approach to combine the information of local likelihood in the smoothing literature.…”

Section: Introductionmentioning

confidence: 96%

Analysis of Deviance in Generalized Partial Linear Models

Härdle

Huang

2013

SSRN Journal

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We develop analysis of deviance tools for generalized partial linear models based on local polynomial fitting. Assuming a canonical link, we propose expressions for both local and global analysis of deviance, which admit an additivity property that reduces to ANOVA decompositions in the Gaussian case. Chi-square tests based on integrated likelihood functions are proposed to formally test whether the nonparametric term is significant. Simulation results are shown to illustrate the proposed chi-square tests. The methodology is applied to German Bundesbank Federal Reserve data.

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Integrated likelihood functions for non-Bayesian inference

Cited by 43 publications

References 21 publications

Adjustments of profile likelihood through predictive densities

Adjustments of profile likelihood through predictive densities

On interval and point estimators based on a penalization of the modified profile likelihood

Analysis of Deviance in Generalized Partial Linear Models

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