TY  - JOUR
ID  - Wojdyła2021
LB  - Wojdyła2021
AU  - Wojdyła, Jakub
TI  - Nonparametric bootstrap confidence bands for unfolding sphere size distributions
ST  - Nonparametric bootstrap confidence bands for unfolding sphere size distributions
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2021
VL  - 41
IS  - 5
SP  - 725
EP  - 740
DO  - https://doi.org/10.7494/OpMath.2021.41.5.725
UR  - https://doi.org/10.7494/OpMath.2021.41.5.725
AB  - 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.
KW  - bootstrap
KW  - confidence bands
KW  - inverse problem
KW  - nonparametric density estimation
KW  - Wicksell's problem
SN  - 1232-9274
ER  -