Methods for density estimation in thick-slice versions of Wicksells problem
Date
2000
Authors
Feuerverger, Andrey
Hall, Peter
Journal Title
Journal ISSN
Volume Title
Publisher
American Statistical Association
Abstract
A new, implicit method is suggested for density estimation in inverse problems, where data are drawn not from the target distribution, hut rather from its image under a transformation. The approach that we propose produces density estimators that are themselves densities, without the negativity problems known to plague more explicit inversion techniques. We also suggest a general empirical approach to selecting the smoothing parameter so as to optimize performance in the context of the target distribution, rather than its image after the transformation. We apply the new methods, and competing techniques, to a thick-section Wicksell-type problem, using data on the radii of nerve terminals from the electric organ of the electric ray Torpedo marmorata. It is shown that statistical properties of estimators in this problem are very different from those for the thin-slice, classical Wicksell problem, and so the two cases cannot be developed simply by analogy with one another.
Description
Keywords
Keywords: Bandwidth; Binwidth; Frequency polygon; Histogram; Ill-posed problem; Inverse problem; Kernel methods; Radius; Sphere; Stereology; Thick slice; Thin slice; Volterra equation
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Source
Journal of the American Statistical Association
Type
Journal article