Opuscula Math. 30, no. 2 (), 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

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.