Sharp adaptation for inverse problems with random noise

Research Report SRR00-001

Sharp adaptation for inverse problems with random noise

L. Cavalier and A. B. Tsybakov

Abstract: We consider a heteroscedastic sequence space setup with polynomially increasing variances of observations that allows to treat a number of inverse problems, in particular multivariate ones. We propose an adaptive estimator that attains simultaneously exact asymptotic minimax constants on every ellipsoid of functions within a wide scale (that includes ellipoids with polynomially and exponentially decreasing axes) and, at the same time, satisfies asymptotically exact oracle inequalities within any class of linear estimates having monotone non-decreasing weights. As application, we construct sharp adaptive estimators in the problems of deconvolution and tomography.

This service is maintained by the Mathematical Sciences Institute (MSI)
Comments to webmaster@maths.anu.edu.au URL: http://wwwmaths.anu.edu.au/