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Statistical models: Conventional, penalized and hierarchical likelihood

Author(s): Daniel Commenges

Journal: Statistics Surveys
ISSN 1935-7516

Volume: 3;
Start page: 1;
Date: 2009;
Original page

Keywords: Bayes estimators | Cross-validation | h-likelihood | Incomplete data | Kullback-Leibler risk | Likelihood | Penalized likelihood | Sieves | Statistical models

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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