The integral of a second-order stochastic process $Z$ over a $d$-dimensional domain is estimated by a weighted linear combination of observations of $Z$ in a random design. The design sample points are possibly dependent random variables and are independent of the process $Z$, which may be nonstationary. Necessary and sufficient conditions are obtained for the mean squared error of a random design estimator to converge to zero as the sample size increases towards infinity. Simple random, stratified and systematic sampling designs are considered; an optimal simple random design is obtained for fixed sample size; and the mean squared errors of the estimators from these designs are compared. It is shown, for example, that for any simple random design there is always a better stratified design.
Publié le : 1982-06-14
Classification:
Random designs,
estimation of integrals of stochastic processes,
simple random sampling,
stratified sampling,
systematic sampling,
60G00,
62K05
@article{1176345793,
author = {Schoenfelder, Carol and Cambanis, Stamatis},
title = {Random Designs for Estimating Integrals of Stochastic Processes},
journal = {Ann. Statist.},
volume = {10},
number = {1},
year = {1982},
pages = { 526-538},
language = {en},
url = {http://dml.mathdoc.fr/item/1176345793}
}
Schoenfelder, Carol; Cambanis, Stamatis. Random Designs for Estimating Integrals of Stochastic Processes. Ann. Statist., Tome 10 (1982) no. 1, pp. 526-538. http://gdmltest.u-ga.fr/item/1176345793/