@Article{Podlewski2016,
author = "Podlewski, Jacek and Szkutnik, Zbigniew",
title = "On a dense minimizer of empirical risk in inverse problems",
journal = "Opuscula Math.",
year = "2016",
volume = "36",
number = "5",
pages = "671--679",
doi = "http://dx.doi.org/10.7494/OpMath.2016.36.5.671",
url = "http://dx.doi.org/10.7494/OpMath.2016.36.5.671",
abstract = "Properties of estimators of a functional parameter in an inverse problem setup are studied. We focus on estimators obtained through dense minimization (as opposed to minimization over \(\delta\)-nets) of suitably defined empirical risk. At the cost of imposition of a sort of local finite-dimensionality assumption, we fill some gaps in the proofs of results published by Klemelä and Mammen [Ann. Statist. 38 (2010), 482-511]. We also give examples of functional classes that satisfy the modified assumptions.",
keywords = "inverse problem, empirical risk minimization",
issn = "1232-9274"
}