Open Access
May 2011 Stochastic comparisons of stratified sampling techniques for some Monte Carlo estimators
Larry Goldstein, Yosef Rinott, Marco Scarsini
Bernoulli 17(2): 592-608 (May 2011). DOI: 10.3150/10-BEJ295

Abstract

We compare estimators of the (essential) supremum and the integral of a function $f$ defined on a measurable space when $f$ may be observed at a sample of points in its domain, possibly with error. The estimators compared vary in their levels of stratification of the domain, with the result that more refined stratification is better with respect to different criteria. The emphasis is on criteria related to stochastic orders. For example, rather than compare estimators of the integral of $f$ by their variances (for unbiased estimators), or mean square error, we attempt the stronger comparison of convex order when possible. For the supremum, the criterion is based on the stochastic order of estimators.

Citation

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Larry Goldstein. Yosef Rinott. Marco Scarsini. "Stochastic comparisons of stratified sampling techniques for some Monte Carlo estimators." Bernoulli 17 (2) 592 - 608, May 2011. https://doi.org/10.3150/10-BEJ295

Information

Published: May 2011
First available in Project Euclid: 5 April 2011

zbMATH: 1345.60010
MathSciNet: MR2787606
Digital Object Identifier: 10.3150/10-BEJ295

Keywords: convex loss , Convex order , majorization , stochastic order , stratified sampling

Rights: Copyright © 2011 Bernoulli Society for Mathematical Statistics and Probability

Vol.17 • No. 2 • May 2011
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