Articles

Stochastic comparisons of stratified sampling techniques for some Monte Carlo estimators

L. Goldstein, Y. Rinott, M. SCARSINI

Bernoulli

2011, vol. 17, n°2, pp.592-608

Départements : Economie et Sciences de la décision

Mots clés : Convex loss, Convex order, Majorization, Stochastic order, Stratified sampling


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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