## Sharp Adaptation for Inverse Problems With Random Noise (2000)

Citations: | 41 - 6 self |

### BibTeX

@MISC{Cavalier00sharpadaptation,

author = {L. Cavalier and A.B. Tsybakov},

title = {Sharp Adaptation for Inverse Problems With Random Noise},

year = {2000}

}

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### OpenURL

### 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.