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2009 Statistical models: Conventional, penalized and hierarchical likelihood
Daniel Commenges
Statist. Surv. 3: 1-17 (2009). DOI: 10.1214/08-SS039


We give an overview of statistical models and likelihood, together with two of its variants: penalized and hierarchical likelihood. The Kullback-Leibler divergence is referred to repeatedly in the literature, for defining the misspecification risk of a model and for grounding the likelihood and the likelihood cross-validation, which can be used for choosing weights in penalized likelihood. Families of penalized likelihood and particular sieves estimators are shown to be equivalent. The similarity of these likelihoods with a posteriori distributions in a Bayesian approach is considered.


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Daniel Commenges. "Statistical models: Conventional, penalized and hierarchical likelihood." Statist. Surv. 3 1 - 17, 2009.


Published: 2009
First available in Project Euclid: 7 April 2009

zbMATH: 1190.62072
MathSciNet: MR2520977
Digital Object Identifier: 10.1214/08-SS039

Primary: 62-02 , 62C99
Secondary: 62A01

Keywords: Bayes estimators , cross-validation , h-likelihood , incomplete data , Kullback-Leibler risk , likelihood , penalized likelihood , sieves , statistical models

Rights: Copyright © 2009 The author, under a Creative Commons Attribution License


Vol.3 • 2009
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