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Browsing by Subject "singular value expansion"

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    Item type:Article, Access status: Open Access ,
    Unfolding spheres size distribution from linear sections with B-splines and EMDS algorithm
    (2007) Szkutnik, Zbigniew
    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.