The kernel method for unfolding sphere size distributions
Journal of Computational Physics
Detection, Estimation, and Modulation Theory: Radar-Sonar Signal Processing and Gaussian Signals in Noise
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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.