Support and distribution inference from noisy data - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2023

Support and distribution inference from noisy data

Résumé

We consider noisy observations of a distribution with unknown support. In the deconvolution model, it has been proved recently [19] that, under very mild assumptions, it is possible to solve the deconvolution problem without knowing the noise distribution and with no sample of the noise. We first give general settings where the theory applies and provide classes of supports that can be recovered in this context. We then exhibit classes of distributions over which we prove adaptive minimax rates (up to a log log factor) for the estimation of the support in Hausdorff distance. Moreover, for the class of distributions with compact support, we provide estimators of the unknown (in general singular) distribution and prove maximum rates in Wasserstein distance. We also prove an almost matching lower bound on the associated minimax risk.
Fichier principal
Vignette du fichier
Manifold_estimation.pdf (690.2 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-04073724 , version 1 (19-04-2023)

Identifiants

  • HAL Id : hal-04073724 , version 1

Citer

Jeremie Capitao-Miniconi, Élisabeth Gassiat, Luc Lehéricy. Support and distribution inference from noisy data. 2023. ⟨hal-04073724⟩
72 Consultations
41 Téléchargements

Partager

Gmail Facebook X LinkedIn More