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- W2035380381 abstract "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." @default.
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- W2035380381 date "1982-06-01" @default.
- W2035380381 modified "2023-09-23" @default.
- W2035380381 title "Random Designs for Estimating Integrals of Stochastic Processes" @default.
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- W2035380381 doi "https://doi.org/10.1214/aos/1176345793" @default.
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