Statistical models, likelihood, penalized likelihood and hierarchical likelihood

Details Statistical models, likelihood, penalized likelihood and hierarchical likelihood Statistical models, likelihood, penalized likelihood and hierarchical likelihood

2008-08-29

arxiv.org/abs/0808.4042v1

Mathematics

Statistics Theory

Submitted to the Statistics Surveys (http://www.i-journals.org/ss/) by the Institute of Mathematical Statistics (http://www.im

Scientific paper

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, for defining the misspecification risk of a model, for grounding the likelihood and the likelihood crossvalidation which can be used for choosing weights in penalized likelihood. Families of penalized likelihood and sieves estimators are shown to be equivalent. The similarity of these likelihood with a posteriori distributions in a Bayesian approach is considered.

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