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

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Author(s): Zbigniew Szkutnik

Journal: Opuscula Mathematica
ISSN 1232-9274

Volume: 27;
Issue: 1;
Start page: 151;
Date: 2007;
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Keywords: inverse problem | singular value expansion | stereology | discretization | quasi-maximum likelihood estimator

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.
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