OPTIMAL MODEL SELECTION IN HETEROSCEDASTIC REGRESSION USING STRONGLY LOCALISED BASES - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2015

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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Dates et versions

hal-00528539 , version 1 (22-10-2010)
hal-00528539 , version 2 (27-03-2011)
hal-00528539 , version 3 (20-05-2015)
hal-00528539 , version 4 (02-09-2016)
hal-00528539 , version 5 (21-03-2017)

Identifiants

Citer

Adrien Saumard. OPTIMAL MODEL SELECTION IN HETEROSCEDASTIC REGRESSION USING STRONGLY LOCALISED BASES. 2015. ⟨hal-00528539v3⟩
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