Open Access
June, 1982 Random Designs for Estimating Integrals of Stochastic Processes
Carol Schoenfelder, Stamatis Cambanis
Ann. Statist. 10(2): 526-538 (June, 1982). DOI: 10.1214/aos/1176345793


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.


Download Citation

Carol Schoenfelder. Stamatis Cambanis. "Random Designs for Estimating Integrals of Stochastic Processes." Ann. Statist. 10 (2) 526 - 538, June, 1982.


Published: June, 1982
First available in Project Euclid: 12 April 2007

zbMATH: 0492.62075
MathSciNet: MR653527
Digital Object Identifier: 10.1214/aos/1176345793

Primary: 60G00
Secondary: 62K05

Keywords: estimation of integrals of stochastic processes , Random designs , simple random sampling , stratified sampling , systematic sampling

Rights: Copyright © 1982 Institute of Mathematical Statistics

Vol.10 • No. 2 • June, 1982
Back to Top