This article is cited in 2 papers

Methods of Signal Processing

Asymptotically Efficient Smoothing in the Wicksell Problem under Squared Losses

G. K. Golubev, F. N. Enikeeva


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.

UDC: 621.391.1:519.2

Received: 17.05.2000
Revised: 28.09.2000

 English version: Problems of Information Transmission, 2001, 37:1, 24–45

Bibliographic databases:

• 
•