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Limiting distributions for minimum relative entropy calibration

Part of: Communication, information Probabilistic methods, simulation and stochastic differential equations Mathematical economics Limit theorems

Published online by Cambridge University Press:  14 July 2016

Łukasz Kruk
Łukasz Kruk*
Affiliation:
Maria Curie-Skłodowska University, Lublin
*
∗ Postal address: Institute of Mathematics, Maria Curie-Skłodowska University, Lublin, Poland. Email address: lkruk@hektor.umcs.lublin.pl
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Abstract

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.

Keywords

Model calibrationentropyweak convergenceMonte Carlo

MSC classification

Primary: 60F17: Functional limit theorems; invariance principles 91B70: Stochastic models 94A17: Measures of information, entropy
Secondary: 65C05: Monte Carlo methods 65C20: Models, numerical methods

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 41 , Issue 1 , March 2004 , pp. 35 - 50
Copyright
Copyright © Applied Probability Trust 2004 

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