Abstract
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.
Original language | English (US) |
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Pages (from-to) | 251-268 |
Number of pages | 18 |
Journal | Canadian Journal of Statistics |
Volume | 29 |
Issue number | 2 |
DOIs | |
State | Published - Jun 2001 |
Externally published | Yes |
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Statistics, Probability and Uncertainty
Keywords
- Abel integral equation
- Adaptive estimation
- Besov spaces
- Corpuscle problem
- Fractional integration
- Linear estimators
- Wavelet thresholding
- Wavelets