Unfolding spheres size distribution from linear sections with B-splines and EMDS algorithm
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 sie...
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| Format: | Article |
| Language: | English |
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AGH Univeristy of Science and Technology Press
2007-01-01
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| Series: | Opuscula Mathematica |
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| Online Access: | http://www.opuscula.agh.edu.pl/vol27/1/art/opuscula_math_2712.pdf |
| Summary: | 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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| ISSN: | 1232-9274 |