HAL CCSD
Stochastic comparisons of stratified sampling techniques for some Monte Carlo estimators
Scarsini, Marco
Rinott, Yosef
Goldstein, L.
Groupement de Recherche et d'Etudes en Gestion à HEC (GREGH) ; Ecole des Hautes Etudes Commerciales (HEC Paris)-Centre National de la Recherche Scientifique (CNRS)
Department of Mathematics [Univ California Davis] (MATH - UC Davis) ; University of California [Davis] (UC Davis) ; University of California (UC)-University of California (UC)
International audience
ISSN: 1350-7265
Bernoulli
Bernoulli Society for Mathematical Statistics and Probability
hal-00609500
https://hec.hal.science/hal-00609500
https://hec.hal.science/hal-00609500
Bernoulli, 2011, 2 (17), pp.592-608. ⟨10.3150/10-BEJ295⟩
ARXIV: 1005.5414
info:eu-repo/semantics/altIdentifier/arxiv/1005.5414
DOI: 10.3150/10-BEJ295
info:eu-repo/semantics/altIdentifier/doi/10.3150/10-BEJ295
en
convex loss
convex order
majorization
stochastic order
stratified sampling
[SHS.ECO.ECO]Humanities and Social Sciences/Economics and Finance/domain_shs.eco.eco
info:eu-repo/semantics/article
Journal articles
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.
2011-03