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A wavelet method for unfolding sphere size distributions. (English) Zbl 0974.62029
Summary: The authors consider the problem of estimating the density of the radii of spheres in a medium, based on their observed random cross-sections. This problem is known as Wicksell’s corpuscle problem. The authors first convert Wicksell’s integral equation to a form suitable for the application of thresholding wavelet methods to solve ill-posed integral equations, given noisy data. They then derive the asymptotic properties of their estimators and compare them with other methods available via a Monte Carlo simulation study. They also illustrate their approach with some real data.
MSC:
62G07Density estimation
65C05Monte Carlo methods
42C40Wavelets and other special systems
65C60Computational problems in statistics