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We deal with the problem of choosing a piecewise constant estimator of a regression function mapping into .
We consider a non Gaussian regression framework with deterministic design points, and we adopt the non asymptotic approach of model selection penalization developed by Birgé and Massart.
Given a collection of partitions of ,
with possibly exponential complexity,
and the corresponding collection of piecewise constant estimators,
we propose a penalized least squares criterion which...
This paper deals with variable selection in regression and binary classification frameworks. It proposes an automatic and exhaustive procedure which relies on the use of the CART algorithm and on model selection via penalization. This work, of theoretical nature, aims at determining adequate penalties, penalties which allow achievement of oracle type inequalities justifying the performance of the proposed procedure. Since the exhaustive procedure cannot be realized when the number of variables is...
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