Statistica Sinica

Anna Dudek and Zbigniew Szkutnik

Abstract:The stereological problem of unfolding the spheres size distribution from linear sections is analysed as a statistical inverse problem of estimation of a Poisson process intensity function from indirectly observed and binned data. Using suitably constructed singular value decomposition of the folding operator, a spectral estimator is constructed that is, up to a logarithmic factor, asymptotically rate minimax over a Sobolev-type class of functions. Finite sample behaviour of the estimator is demonstrated in a small numerical experiment.

Key words and phrases:Discretization, empirical risk minimization, ill-posed inverse problem, rate minimaxity, singular value decomposition, stereology.