Opuscula Math. 36, no. 5 (2016), 671-679
On a dense minimizer of empirical risk in inverse problems
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.