Autor: Szkutnik, Z. - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: A note on minimax rates of convergence in the Spektor-Lord-Willis problem
Autorzy:: Szkutnik, Z.
Powiązania:: https://bibliotekanauki.pl/articles/254773.pdf
Data publikacji:: 2010
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:: poisson inverse problem
rate minimaxity
singular value decomposition
stereology
Opis:: In this note, attainable lower bounds are constructed for the convergence rates in a stereological problem of unfolding spheres size distribution from linear sections, which shows that a spectral type estimator is strictly rate minimax over some Sobolev-type classes of functions.
Źródło:: Opuscula Mathematica; 2010, 30, 2; 203-207
1232-9274
2300-6919
Pojawia się w:: Opuscula Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: Unfolding spheres size distribution from linear sections with B-splines and EMDS algorithm
Autorzy:: Szkutnik, Z.
Powiązania:: https://bibliotekanauki.pl/articles/255515.pdf
Data publikacji:: 2007
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:: inverse problem
singular value expansion
stereology
discretization
quasi-maximum likelihood estimator
Opis:: The stereological problem of unfolding spheres size distribution from linear sections is formulated as a problem of inverse estimation of a Poisson process intensity function. A singular value expansion of the corresponding integral operator is given. The theory of recently proposed B-spline sieved quasi-maximum likelihood estimators is modified to make it applicable to the current problem. Strong L2-consistency is proved and convergence rates are given. The estimators are implemented with the recently proposed EMDS algorithm. Promising performance of this new methodology in finite samples is illustrated with a numerical example. Data grouping effects are also discussed.
Źródło:: Opuscula Mathematica; 2007, 27, 1; 151-165
1232-9274
2300-6919
Pojawia się w:: Opuscula Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 3.

Tytuł:: On a dense minimizer of empirical risk in inverse problems
Autorzy:: Podlewski, J.
Szkutnik, Z.
Powiązania:: https://bibliotekanauki.pl/articles/952841.pdf
Data publikacji:: 2016
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:: inverse problem
empirical risk minimization
Opis:: 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.
Źródło:: Opuscula Mathematica; 2016, 36, 5; 671-679
1232-9274
2300-6919
Pojawia się w:: Opuscula Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

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