Unfolding spheres size distribution from linear sections with B-splines and EMDS algorithm

Abstract

The stereological problem of unfolding spheres size distribution from linear sections is formulated as a problem of inverse estimation of a Poisson process intensity function. A singular value expansion of the corresponding integral operator is given. The theory of recently proposed $B$-spline sieved quasi-maximum likelihood estimators is modified to make it applicable to the current problem. Strong $L^{2}$-consistency is proved and convergence rates are given. The estimators are implemented with the recently proposed EMDS algorithm. Promising performance of this new methodology in finite samples is illustrated with a numerical example. Data grouping effects are also discussed.