Asymptotically Efficient Smoothing in the Wicksell Problem under Squared Losses

Asymptotically Efficient Smoothing in the Wicksell Problem under Squared Losses In the Wicksell problem, it is required to reconstruct a distribution function of radii of balls located in an opaque medium from measurements of radii of circles obtained by intersecting the medium with a certain plane. This problem is intimately bound up with estimating a fractional derivative of order 1/2 for a distribution function concentrated on the positive semi-axis. In this paper, the locally asymptotically minimax risk in the Wicksell problem is evaluated up to a constant. Estimators on which this risk is attained are also constructed. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Problems of Information Transmission Springer Journals

Asymptotically Efficient Smoothing in the Wicksell Problem under Squared Losses

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Publisher
Kluwer Academic Publishers-Plenum Publishers
Copyright
Copyright © 2001 by MAIK “Nauka/Interperiodica”
Subject
Engineering; Communications Engineering, Networks; Electrical Engineering; Information Storage and Retrieval; Systems Theory, Control
ISSN
0032-9460
eISSN
1608-3253
D.O.I.
10.1023/A:1010495609901
Publisher site
See Article on Publisher Site

Abstract

In the Wicksell problem, it is required to reconstruct a distribution function of radii of balls located in an opaque medium from measurements of radii of circles obtained by intersecting the medium with a certain plane. This problem is intimately bound up with estimating a fractional derivative of order 1/2 for a distribution function concentrated on the positive semi-axis. In this paper, the locally asymptotically minimax risk in the Wicksell problem is evaluated up to a constant. Estimators on which this risk is attained are also constructed.

Journal

Problems of Information TransmissionSpringer Journals

Published: Oct 9, 2004

References

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