Opuscula Mathematica
Opuscula Math. 36, no. 5 (2016), 671-679

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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About the authors ▼
Jacek Podlewski
StatSoft Poland, ul. Kraszewskiego 36, 30-110 Krakow, Poland
Zbigniew Szkutnik
AGH University of Science and Technology, Faculty of Applied Mathematics, al. A. Mickiewicza 30, 30-059 Krakow, Poland
About the article ▼
Communicated by Andrzej Kozek.
Received: 2015-10-15.
Revised: 2016-03-10.
Accepted: 2016-03-10.
Published online: 2016-06-29.
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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