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

Szkutnik Z.

Opuscula Mathematica

2007

Vol. 27, no. 1

151-165

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 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 finite samples is illustrated with a numerical example. Data grouping effects are also discussed.