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Oracle inequalities, aggregation and adaptation

Abstract : Originally, oracle inequalities were developed as particularly efficient tools in mathematical statistics for deriving adaptation to an unknown parameter. Initially dedicated to the demonstration of statistical properties in the study of certain estimators, they can be extrapolated to the broader framework of aggregation in which they constitute the core of the definition of an optimal rate of aggregation. As such, they become not only mathematical tools but also precise finite sample results.
In this thesis, several fields of application of oracle inequalities are presented. They are used first in a general aggregation framework and then in particular statistical models such as nonparametric density estimation, regression and classification. The obtained results map the variety of applications of oracle inequalities in mathematical statistics.
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Contributor : Philippe Rigollet Connect in order to contact the contributor
Submitted on : Tuesday, November 21, 2006 - 3:21:42 PM
Last modification on : Sunday, June 26, 2022 - 5:34:35 AM
Long-term archiving on: : Tuesday, April 6, 2010 - 11:08:43 PM



  • HAL Id : tel-00115494, version 1


Philippe Rigollet. Oracle inequalities, aggregation and adaptation. Mathematics [math]. Université Pierre et Marie Curie - Paris VI, 2006. English. ⟨tel-00115494⟩



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