Opuscula Math. 30, no. 2 (2010), 203-207
http://dx.doi.org/10.7494/OpMath.2010.30.2.203

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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