TY  - JOUR
ID  - Podlewski2016
LB  - Podlewski2016
AU  - Podlewski, Jacek
AU  - Szkutnik, Zbigniew
TI  - On a dense minimizer of empirical risk in inverse problems
ST  - On a dense minimizer of empirical risk in inverse problems
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2016
VL  - 36
IS  - 5
SP  - 671
EP  - 679
DO  - http://dx.doi.org/10.7494/OpMath.2016.36.5.671
UR  - http://dx.doi.org/10.7494/OpMath.2016.36.5.671
AB  - 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.
KW  - inverse problem
KW  - empirical risk minimization
SN  - 1232-9274
ER  -