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Semiparametric cross entropy for rare-event simulation

Part of: Probabilistic methods, simulation and stochastic differential equations

Published online by Cambridge University Press:  24 October 2016

Z. I. Botev ,
A. Ridder  and
L. Rojas-Nandayapa
Z. I. Botev*
Affiliation:
The University of New South Wales
A. Ridder*
Affiliation:
Vrije Universiteit
L. Rojas-Nandayapa*
Affiliation:
The University of Queensland
*
*Postal address: School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia. Email address: [email protected]
** Postal address: School of Mathematics and Physics, The University of Queensland, Brisbane, QLD 4072, Australia.
*** Postal address: Department of Econometrics and Operations Research, Vrije Universiteit, 1081 HV, Amsterdam, The Netherlands.
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Abstract

The cross entropy is a well-known adaptive importance sampling method which requires estimating an optimal importance sampling distribution within a parametric class. In this paper we analyze an alternative version of the cross entropy, where the importance sampling distribution is selected instead within a general semiparametric class of distributions. We show that the semiparametric cross entropy method delivers efficient estimators in a wide variety of rare-event problems. We illustrate the favourable performance of the method with numerical experiments.

Keywords

Light-tailedregularly-varyingsubexponentialrare-event probabilitycross entropy method

MSC classification

Primary: 65C05: Monte Carlo methods
Secondary: 65C60: Computational problems in statistics 65C40: Computational Markov chains
Type
Research Papers
Information
Journal of Applied Probability , Volume 53 , Issue 3 , September 2016 , pp. 633 - 649
Copyright
Copyright © Applied Probability Trust 2016 

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