We consider the classical Wicksell problem of estimating an unknown
distribution function $G$of the radii of balls, based on their observed
crosssections. It is assumed that the underlying distribution function$G$
belongs to a Hölder class of smoothness $\gamma >1/2$. We prove that,
for a suitable choice of the smoothing parameters, kernel-type estimators are
asymptotically efficient for a large class of symmetric bowl-shaped loss
functions.
Publié le : 1998-12-14
Classification:
Wicksell’s problem,
Hölder classes,
fractional derivatives,
kernel density estimators,
62G05,
62G20,
62C20,
62E20
@article{1024691477,
author = {Golubev, G. K. and Levit, B. Y.},
title = {Asymptotically efficient estimation in the Wicksell
problem},
journal = {Ann. Statist.},
volume = {26},
number = {3},
year = {1998},
pages = { 2407-2419},
language = {en},
url = {http://dml.mathdoc.fr/item/1024691477}
}
Golubev, G. K.; Levit, B. Y. Asymptotically efficient estimation in the Wicksell
problem. Ann. Statist., Tome 26 (1998) no. 3, pp. 2407-2419. http://gdmltest.u-ga.fr/item/1024691477/