The problem is to estimate sequentially a nonparametric function known to belong to an $\alpha$-th-order Sobolev subspace $(\alpha > \frac{1}{2})$ with a minimax mean stopping time subject to an assigned maximum mean integrated squared error. For the case of a given $\alpha$ there exists a sharp estimator which has a minimal constant and a rate of minimax mean stopping time increasing as the assigned risk decreases. The situation changes drastically if $\alpha$ is unknown: a necessary and sufficient condition for sharp estimation is that $\gamma < \alpha \leq 2\gamma$ for some given $\gamma \geq \frac{1}{2}$.
Publié le : 1995-08-14
Classification:
Sequential estimation,
minimax,
stopping time,
curve fitting,
62G05,
62G07,
62E20,
62F12,
62J02
@article{1176324713,
author = {Efromovich, Sam},
title = {Sequential Nonparametric Estimation with Assigned Risk},
journal = {Ann. Statist.},
volume = {23},
number = {6},
year = {1995},
pages = { 1376-1392},
language = {en},
url = {http://dml.mathdoc.fr/item/1176324713}
}
Efromovich, Sam. Sequential Nonparametric Estimation with Assigned Risk. Ann. Statist., Tome 23 (1995) no. 6, pp. 1376-1392. http://gdmltest.u-ga.fr/item/1176324713/