Stochastic comparisons of stratified sampling techniques for some Monte Carlo estimators

Marco Scarsini, Yosef Rinott and L. Goldstein

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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.

Keywords: convex loss; convex order; majorization; stochastic order; stratified sampling (search for similar items in EconPapers)
Date: 2011-03
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Published in Bernoulli, 2011, 2 (17), pp.592-608. ⟨10.3150/10-BEJ295⟩

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Related works:
Working Paper: Stochastic comparisons of stratifed sampling techniques for some Monte Carlo estimators (2010)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-00609500

DOI: 10.3150/10-BEJ295

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