A characterisation of isometries with respect to the Lévy-Prokhorov metric

We consider minimum relative entropy calibration of a given prior distribution to a finite set of moment constraints. We show that the calibration algorithm is stable (in the Prokhorov metric) under a perturbation of the prior and the calibrated distributions converge in variation to the measure from which the moments have been taken as more constraints are added. These facts are used to explain the limiting properties of the minimum relative entropy Monte Carlo calibration algorithm.

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An Estimate of the Lévy–Prokhorov Metric

Theory of Probability and Its Applications ◽

10.1137/1129009 ◽

1985 ◽

Vol 29 (1) ◽

pp. 109-114 ◽

Cited By ~ 6

Author(s):

V. V. Senatov

Keyword(s):

Prokhorov Metric

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Limiting distributions for minimum relative entropy calibration

Journal of Applied Probability ◽

10.1239/jap/1077134666 ◽

2004 ◽

Vol 41 (1) ◽

pp. 35-50 ◽

Cited By ~ 1

Author(s):

Łukasz Kruk

Keyword(s):

Monte Carlo ◽

Relative Entropy ◽

Prior Distribution ◽

Limiting Distributions ◽

Prokhorov Metric ◽

Finite Set ◽

Calibration Algorithm ◽

Minimum Relative Entropy

We consider minimum relative entropy calibration of a given prior distribution to a finite set of moment constraints. We show that the calibration algorithm is stable (in the Prokhorov metric) under a perturbation of the prior and the calibrated distributions converge in variation to the measure from which the moments have been taken as more constraints are added. These facts are used to explain the limiting properties of the minimum relative entropy Monte Carlo calibration algorithm.

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Superresolution Rates in Prokhorov Metric

Canadian Journal of Mathematics ◽

10.4153/cjm-1996-017-9 ◽

1996 ◽

Vol 48 (2) ◽

pp. 316-329 ◽

Cited By ~ 8

Author(s):

P. Doukhan ◽

F. Gamboa

Keyword(s):

Continuous Function ◽

Probability Measure ◽

Convex Hull ◽

Compact Subset ◽

Prokhorov Metric ◽

System Extension

AbstractConsider the problem of recovering a probability measure supported by a compact subsetUof ℝmwhen the available measurements concern only some of its Ф-moments (Ф being an ℝkvalued continuous function onU). When thetrueФ-momentclies on the boundary of the convex hull of Ф(U), generalizing the results of [10], we construct asmallsetRα,δ(∊)such that any probability measureμsatisfyingisalmostconcentrated onRα,δ(∊). When Ф is a pointwiseT-system (extension ofT-systems), the study of the setRα,δ(∊)leads to the evaluation of the Prokhorov radius of the set.

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