Opuscula Math. 30, no. 2 (2010), 203-207

Opuscula Mathematica

A note on minimax rates of convergence in the Spektor-Lord-Willis problem

Zbigniew Szkutnik

Abstract. 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.

Keywords: Poisson inverse problem, rate minimaxity, singular value decomposition, stereology.

Mathematics Subject Classification: 62G05, 65J22.

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  • Zbigniew Szkutnik
  • AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Krakow, Poland
  • Received: 2009-11-12.
  • Accepted: 2009-11-30.
Opuscula Mathematica - cover

Cite this article as:
Zbigniew Szkutnik, A note on minimax rates of convergence in the Spektor-Lord-Willis problem, Opuscula Math. 30, no. 2 (2010), 203-207, http://dx.doi.org/10.7494/OpMath.2010.30.2.203

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