Model selection in density estimation via cross-validation
Year: 2008
Type: preprint
Abstract: The problem of model selection by cross-validation is addressed in the density estimation framework. Extensively used in practice, cross-validation (CV) remains poorly understood, especially in the non-asymptotic setting which is the main concern of this work. A recurrent problem with CV is the computation time it involves. This drawback is overcome here thanks to closed-form expressions for the CV estimator of the risk for a broad class of widespread estimators: projection estimators. In order to shed new lights on CV procedures with respect to the cardinality $p$ of the test set, the CV estimator is interpreted as a penalized criterion with a random penalty. For instance, the amount of penalization is shown to increase with $p$. A theoretical assessment of the CV performance is carried out thanks to two oracle inequalities applying to respectively bounded or square-integrable densities. For several collections of models, adaptivity results with respect to Holder and Besov spaces are derived as well.
Source: arXiv (Cornell University)
Author: Alain Célisse
Institution: Mathématiques et Informatique Appliquées
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1545606438