Hostname: page-component-cb9f654ff-d5ftd Total loading time: 0 Render date: 2025-08-20T09:15:40.812Z Has data issue: false hasContentIssue false
  • English
  • Français

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: botev@unsw.edu.au
** 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.
Get access Rights & Permissions [Opens in a new window]

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

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 53 , Issue 3 , September 2016 , pp. 633 - 649
Copyright
Copyright © Applied Probability Trust 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

[1] Asmussen, S. and Glynn, P. W. (2007).Stochastic Simulation: Algorithms and Analysis,Springer,New York.Google Scholar
[2] Asmussen, S. and Kroese, D. P. (2006).Improved algorithms for rare event simulation with heavy tails.Adv. Appl. Prob. 38,545–558.Google Scholar
[3] Asmussen, S.,Kroese, D. P. and Rubinstein, R. Y. (2005).Heavy tails, importance sampling and cross-entropy.Stoch. Models 21,57–76.Google Scholar
[4] Botev, Z. I. and Kroese, D. P. (2012).Efficient Monte Carlo simulation via the generalized splitting method.Statist. Comput. 22,1–16.Google Scholar
[5] Botev, Z. I.,L'Ecuyer, P. and Tuffin, B. (2013).Markov chain importance sampling with applications to rare event probability estimation.Statist. Comput. 23,271–285.Google Scholar
[6] Chan, J. C. C.,Glynn, P. W. and Kroese, D. P. (2011).A comparison of cross-entropy and variance minimization strategies. In New Frontiers in Applied Probability (J. Appl. Prob. Spec. Vol. 48A),New Frontiers in Applied Probability Applied Probability Trust,Sheffield, pp.183–194.Google Scholar
[7] Dupuis, P. Leder, K. Wang, H. (2007).Importance sampling for sums of random variables with regularly varying tails.ACM TOMACS 17,14.Google Scholar
[8] Embrechts, P. and Goldie, C. M. (1980).On closure and factorization properties of subexponential and related distributions.J. Austral. Math. Soc. A 29,243–256.Google Scholar
[9] Embrechts, P.,Kluppelberg, C. and Mikosch, T. (1997).Modelling Extremal Events.Springer,Berlin.Google Scholar
[10] Foss, S.,Korshunov, D. and Zachary, S. (2011).An Introduction to Heavy-Tailed and Subexponential Distributions,Springer,New York.Google Scholar
[11] Ghamami, S. and Ross, S. M. (2012). Improving the Asmussen–Kroese-type simulation estimators.J. Appl. Prob. 49,1188–1193.Google Scholar
[12] Gudmundsson, T. and Hult, H. (2014).Markov chain Monte Carlo for computing rare-event probabilities for a heavy-tailed random walk.J. Appl. Prob. 51,359–376.Google Scholar
[13] Juneja, S. (2007).Estimating tail probabilities of heavy tailed distributions with asymptotically zero relative error.Queueing Systems 57,115–127.Google Scholar
[14] Perrakis, K.,Ntzoufras, I. and Tsionas, E. G. (2014).On the use of marginal posteriors in marginal likelihood estimation via importance sampling.Comput. Statist. Data Anal. 77,54–69.Google Scholar
[15] Wong, R.(2001).Asymptotic Approximation of Integrals (Classics Appl. Math. 34).Society for Industrial and Applied Mathematics,Philidelphia, PA..Google Scholar