Stochastic comparisons of stratified sampling techniques for some Monte Carlo estimators

Details Stochastic comparisons of stratified sampling techniques for some Monte Carlo estimators Stochastic comparisons of stratified sampling techniques for some Monte Carlo estimators

2010-05-28

arxiv.org/abs/1005.5414v2

Bernoulli 2011, Vol. 17, No. 2, 592-608

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.3150/10-BEJ295 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statisti

Scientific paper

10.3150/10-BEJ295

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.

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