OPTIMAL MODEL SELECTION IN HETEROSCEDASTIC REGRESSION USING STRONGLY LOCALISED BASES

Adrien Saumard (1)

1 CIMFAV - Centro de Investigación y Modelamiento de Fenómenos Aleatorios – Valparaíso

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.

Mots clés: slope heuristics; hold- out; heteroscedastic noise; model selection; nonparametric regression

Domaines: Théorie [stat.TH]; Méthodologie [stat.ME]

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