Adaptive goodness-of-fit testing from indirect observations - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques Année : 2009

Adaptive goodness-of-fit testing from indirect observations

Résumé

In a convolution model, we observe random variables whose distribution is the convolution of some unknown density $f$ and some known noise density $g$. We assume that $g$ is polynomially smooth. We provide goodness-of-fit testing procedures for the test $H_0:f=f_0$, where the alternative $H_1$ is expressed with respect to $\mathbb{L}_2$-norm (\emph{i.e.} has the form $\psi_{n}^{-2}\|f-f_0\|_2^2 \ge \mathcal{C}$). Our procedure is adaptive with respect to the unknown smoothness parameter $\tau$ of $f$. Different testing rates ($\psi_n$) are obtained according to whether $f_0$ is polynomially or exponentially smooth. A price for adaptation is noted and for computing this, we provide a non-uniform Berry-Esseen type theorem for degenerate $U$-statistics. In the case of polynomially smooth $f_0$, we prove that the price for adaptation is optimal. We emphasise the fact that the alternative may contain functions smoother than the null density to be tested, which is new in the context of goodness-of-fit tests.
Fichier principal
Vignette du fichier
BMP_final.pdf (281.29 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00591200 , version 1 (07-05-2011)

Identifiants

Citer

Cristina Butucea, Catherine Matias, Christophe Pouet. Adaptive goodness-of-fit testing from indirect observations. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2009, 45 (2), pp.352-372. ⟨10.1214/08-AIHP166⟩. ⟨hal-00591200⟩
258 Consultations
95 Téléchargements

Altmetric

Partager

Gmail Mastodon Facebook X LinkedIn More