Opuscula Math. 41, no. 5 (2021), 725-740
https://doi.org/10.7494/OpMath.2021.41.5.725
Opuscula Mathematica
Nonparametric bootstrap confidence bands for unfolding sphere size distributions
Abstract. The stereological inverse problem of unfolding the distribution of spheres radii from measured planar sections radii, known as the Wicksell's corpuscle problem, is considered. The construction of uniform confidence bands based on the smoothed bootstrap in the Wicksell's problem is presented. Theoretical results on the consistency of the proposed bootstrap procedure are given, where the consistency of the bands means that the coverage probability converges to the nominal level. The finite-sample performance of the proposed method is studied via Monte Carlo simulations and compared with the asymptotic (non-bootstrap) solution described in literature.
Keywords: bootstrap, confidence bands, inverse problem, nonparametric density estimation, Wicksell's problem.
Mathematics Subject Classification: 45Q05, 62G05, 62G15, 62G20.
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- Jakub Wojdyła
https://orcid.org/0000-0003-1892-8248- AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Kraków, Poland
- Communicated by Mirosław Pawlak.
- Received: 2021-03-15.
- Accepted: 2021-09-04.
- Published online: 2021-09-30.
