Thresholding procedure with priors based on Pareto distributions

Vincent Rivoirard (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

In this paper, we consider wavelet thresholding rules within a Bayesian framework. The prior imposed on the wavelet coefficients is based upon a Pareto distribution. We introduce weak Besov spaces that enable us to measure the sparsity of each estimated signal. At first, we establish a relationship between the parameters of the prior and the parameters of the weak Besov space in which the realizations built from the prior lie. Subsequently, we exhibit a thresholding rule which threshold at each resolution level depends on the prior parameters. It is compared to deterministic classical thresholding procedures (VisuShrink and SureShrink) but also to efficient Bayesian thresholding algorithms.

Mots clés: Adaptive estimation; Bayesian model; Pareto distribution; sparsity; wavelet thresholding; weak Besov spaces

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

Vincent Rivoirard. Thresholding procedure with priors based on Pareto distributions. Test, 2004, 13 (1), pp.213-246. ⟨10.1007/BF02603007⟩. ⟨hal-00634277⟩