Nonparametric bootstrap confidence bands for unfolding sphere size distributions

Opuscula Mathematica

article

Jakub Wojdyła¹ 

[1] AGH University of Science and Technology, Faculty of Applied Mathematics

关键词: bootstrap;    confidence bands;    inverse problem;    nonparametric density estimation;    Wicksell's problem.;   

DOI  :  10.7494/OpMath.2021.41.5.725

学科分类：环境科学（综合）

来源: AGH University of Science and Technology Press

【 摘 要 】

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.

【 授权许可】

CC BY-NC