On a dense minimizer of empirical risk in inverse problems

• Autorzy: Podlewski J. , Szkutnik Z.

Identyfikatory

DOI

10.7494/OpMath.2016.36.5.671

• Języki publikacji: EN

Abstrakty

EN

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 δ-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 Klemela and Mammen [Ann. Statist. 38 (2010), 482-511]. We also give examples of functional classes that satisfy the modified assumptions.

Słowa kluczowe

EN

inverse problem; empirical risk minimization

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2016
• Tom: Vol. 36, no. 5
• Strony: 671--679
• Opis fizyczny: Bibliogr. 15 poz.

Twórcy

autor

Podlewski J.

• StatSoft Poland ul. Kraszewskiego 36 30-110 Krakow, Poland

autor

Szkutnik Z.

• AGH University of Science and Technology Faculty of Applied Mathematics al. Mickiewicza 30, 30-059 Krakow, Poland

Bibliografia

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Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.