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Biometrika 1990 77(1):139-145;
© 1990 by Biometrika Trust
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Kernel estimation in Wicksell's corpuscle problem

BERT VAN ES and ADRIAAN HOOGENDOORN

Department of Mathematics, Catholic University Toernooiveld, 6525 ED Nymegen, The Netherlands
Central Bureau of Statistics Prinses Beatrixlaan 428, 2273 XZ Voorburg, The Netherlands

Received for publication 1 July 1988. Revision received 1 July 1989.
  Abstract

We consider the estimation of the probability density function of the radii of spheres in a medium, given the radii of their profiles in a random cross-section. This problem is known as Wicksell's corpuscle problem. We present a new estimator related to the classical kernel density estimator and discuss its properties. A comparison is made with other estimators related to the kernel estimator.

Key Words: Kernel density estimator • Particle size distribution • Stereology


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