We study linear estimators for the weighted integral of a stochastic process. The process may only be observed on a finite sampling design. The error is defined in a mean square sense, and the process is assumed to satisfy Sacks-Ylvisaker regularity conditions of order $r \epsilon \mathbb{N}_0$. We show that sampling at the quantiles of a particular density already yields asymptotically optimal estimators. Hereby we extend the results of Sacks and Ylvisaker for regularity $r = 0$ or 1, and we confirm a conjecture by Eubank, Smith and Smith.
Publié le : 1996-10-14
Classification:
Integral estimation,
asymptotically optimal designs,
regular sequence designs,
Sacks-Ylvisaker conditions,
62K05,
41A55,
60G12,
62M99,
65D30
@article{1069362311,
author = {Ritter, Klaus},
title = {Asymptotic optimality of regular sequence designs},
journal = {Ann. Statist.},
volume = {24},
number = {6},
year = {1996},
pages = { 2081-2096},
language = {en},
url = {http://dml.mathdoc.fr/item/1069362311}
}
Ritter, Klaus. Asymptotic optimality of regular sequence designs. Ann. Statist., Tome 24 (1996) no. 6, pp. 2081-2096. http://gdmltest.u-ga.fr/item/1069362311/