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

• Main Author: Zbigniew Szkutnik
• Format: Article
• Language: English
• Published: AGH Univeristy of Science and Technology Press 2007-01-01
• Series: Opuscula Mathematica
• Subjects: inverse problem; singular value expansion; stereology; discretization; quasi-maximum likelihood estimator
• Online Access: http://www.opuscula.agh.edu.pl/vol27/1/art/opuscula_math_2712.pdf

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.