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Abstract: We compare estimators of the essential supremum and the integral of afunction $f$ defined on a measurable space when $f$ may be observed at a sampleof points in its domain, possibly with error. The estimators compared vary intheir levels of stratification of the domain, with the result that more refinedstratification is better with respect to different criteria. The emphasis is oncriteria related to stochastic orders. For example, rather than compareestimators of the integral of $f$ by their variances for unbiased estimators,or mean square error, we attempt the stronger comparison of convex order whenpossible. For the supremum, the criterion is based on the stochastic order ofestimators.



Autor: Larry Goldstein, Yosef Rinott, Marco Scarsini

Fuente: https://arxiv.org/







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