Stochastic comparisons of stratied sampling techniques for some Monte Carlo estimators

Scarsini, Marco and Rinott, Yosef and Goldstein, Larry (2009) Stochastic comparisons of stratied sampling techniques for some Monte Carlo estimators. [Technical Report]. p. 22. (Submitted)

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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 dierent 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. For some of the results no regularity assumptions for "f" are needed, while for others we assume that "f" is monotone on an appropriate domain. Along the way we prove convex order inequalities that are of interest "per se".

Item Type:Report / Paper (Technical Report)
Research documents and activity classification:Working Papers > Non-Refereed Working Papers / of national relevance only
Divisions:Department of Business and Management
Uncontrolled Keywords:Convex order. Stochastic order. Majorization. Stratified sampling.
MIUR Scientific Area:Area 13 - Economics and Statistics > SECS-S/01 Statistics
Deposited By:Chiara Annulli (admin)
Deposited On:28 Oct 2009 12:11
Last Modified:05 Apr 2013 23:18

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