@Article{Szkutnik2007,
author = "Szkutnik, Zbigniew",
title = "Unfolding spheres size distribution from linear sections with B-splines and EMDS algorithm",
journal = "Opuscula Math.",
year = "2007",
volume = "27",
number = "1",
pages = "151--165",
doi = "http://dx.doi.org/10.7494/OpMath.2007.27.1.151",
url = "http://dx.doi.org/10.7494/OpMath.2007.27.1.151",
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.",
keywords = "inverse problem, singular value expansion, stereology, discretization, quasi-maximum likelihood estimator",
issn = "1232-9274"
}