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Bounded Relative Error Importance Sampling and Rare Event Simulation

Published online by Cambridge University Press:  09 August 2013

Don L. McLeish
Don L. McLeish*
Affiliation:
Department of Statistics and Actuarial Science, University of Waterloo, Canada
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Abstract

We consider estimating tail events using exponential families of importance sampling distributions. When the cannonical sufficient statistic for the exponential family mimics the tail behaviour of the underlying cumulative distribution function, we can achieve bounded relative error for estimating tail probabilities. Examples of rare event simulation from various distributions including Tukey's g&h distribution are provided.

Keywords

Rare event simulationrelative errorg&h distributionMonte Carlo methodsImportance samplingCross-entropyRényi Divergence
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 40 , Issue 1 , May 2010 , pp. 377 - 398
Copyright
Copyright © International Actuarial Association 2010

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