Optimal model selection for stationary data under various mixing conditions

Matthieu Lerasle (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

We build penalized least-squares estimators of the marginal density of a stationary process, using the slope algorithm and resampling penalties. When the data are $\beta$ or $\tau$-mixing, these estimators satisfy oracle inequalities with leading constant asymptotically equal to $1$.

Mots clés: weak dependence; Density estimation; optimal model selection; resampling methods; slope heuristic; weak dependence.

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

Matthieu Lerasle. Optimal model selection for stationary data under various mixing conditions. Annals of Statistics, 2012, 39 (4), pp.1852-1877. ⟨10.1214/11-AOS888SUPP⟩. ⟨hal-00430463⟩