Efficient robust sequential analysis for autoregressive big data models

Ouerdia Arkoun (1, 2) , Jean-Yves Brua (2) , Serguei Pergamenshchikov (2)

1 Sup'Biotech
2 LMRS - Laboratoire de Mathématiques Raphaël Salem

In this paper we study high dimension models based on dependent observations defined through autoregressive processes. For such models we study the efficient robust estimation problem in adaptive settings, i.e. in the case when the nonparametric regularity is unknown. To this end we use the sequential model selection procedures proposed in [4]. First, through the Van Trees inequality, we obtain the sharp lower bound for robust risks in explicit form, i.e. the famous Pinsker's constant (see [28] for example). Then, through sharp non asymptotic oracle inequalities for robust risks, we show that the upper bound for the robust risk of the proposed model selection sequential procedure coincides with the obtained Pinsker constant, i.e. this means that this procedure is efficient in the minimax sens.

Mots clés: Non-parametric estimation; Non parametric autoregresion; Nonasymptotic estimation; Robust risk; Model selection; Sharp oracle inequalities

Domaines: Statistiques [stat]; Théorie [stat.TH]

Ouerdia Arkoun, Jean-Yves Brua, Serguei Pergamenshchikov. Efficient robust sequential analysis for autoregressive big data models. 2021. ⟨hal-03154295⟩