Opuscula Math. 36, no. 5 (2016), 671-679
http://dx.doi.org/10.7494/OpMath.2016.36.5.671

Opuscula Mathematica

# On a dense minimizer of empirical risk in inverse problems

Jacek Podlewski
Zbigniew Szkutnik

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.

Mathematics Subject Classification: 62G07.

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Cite this article as:
Jacek Podlewski, Zbigniew Szkutnik, On a dense minimizer of empirical risk in inverse problems, Opuscula Math. 36, no. 5 (2016), 671-679, http://dx.doi.org/10.7494/OpMath.2016.36.5.671

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