UNFOLDING SPHERES SIZE DISTRIBUTION FROM LINEAR SECTIONS WITH B-SPLINES AND EMDS ALGORITHM

Abstract. The stereological problem of unfolding spheres size distribution from linear sec-tions 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 modied to make it applicable to the current problem. Strong L2-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 nite samples is illustrated with a nu-merical example. Data grouping eects are also discussed