Opuscula Math. 30, no. 2 (2010), 203-207
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.
- Received: 2009-11-12.
- Accepted: 2009-11-30.