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Statistical models: Conventional, penalized and hierarchical likelihood

Daniel Commenges 1, * 
Abstract : 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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Submitted on : Friday, April 3, 2009 - 4:30:41 PM
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Daniel Commenges. Statistical models: Conventional, penalized and hierarchical likelihood. Statistics Surveys, Institute of Mathematical Statistics (IMS), 2009, 3, pp.1-17. ⟨10.1214/08-SS039⟩. ⟨inserm-00373280⟩



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