OPTIMAL MODEL SELECTION IN HETEROSCEDASTIC REGRESSION USING STRONGLY LOCALISED BASES
Résumé
We investigate optimality of model selection procedures in regard to the least-squares loss in a heteroscedatic with random design regression context. For the selection of some linear models endowed with a localized basis, as for some Haar expansions, we show the optimality of a data-driven penalty calibration procedure, the so-called slope heuristics. By doing so, we exhibit a minimal penalty being half of the optimal one. The optimal penalty shape being unknown in general, we also propose a hold-out penalization procedure and show that the latter is asymptotically optimal.
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