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
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.
- 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.
