Deconvolution of spherical data corrupted with unknown noise

Autor:	Capitao-Miniconi, Jérémie, Gassiat, Elisabeth
Rok vydání:	2022
Předmět:	Mathematics - Statistics Theory
Druh dokumentu:	Working Paper
Popis:	We consider the deconvolution problem for densities supported on a $(d-1)$-dimensional sphere with unknown center and unknown radius, in the situation where the distribution of the noise is unknown and without any other observations. We propose estimators of the radius, of the center, and of the density of the signal on the sphere that are proved consistent without further information. The estimator of the radius is proved to have almost parametric convergence rate for any dimension $d$. When $d=2$, the estimator of the density is proved to achieve the same rate of convergence over Sobolev regularity classes of densities as when the noise distribution is known. Comment: 25 pages, 6 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2203.00654 Zobrazit plný text záznamu View this record from Arxiv