Skip to main content

Semiparametric cross entropy for rare-event simulation

  • Z. I. Botev (a1), A. Ridder (a2) and L. Rojas-Nandayapa (a3)

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.

Corresponding author
*Postal address: School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia. Email address:
** 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.
Hide All
[1] Asmussen S. and Glynn P. W. (2007).Stochastic Simulation: Algorithms and Analysis,Springer,New York.
[2] Asmussen S. and Kroese D. P. (2006).Improved algorithms for rare event simulation with heavy tails.Adv. Appl. Prob. 38,545558.
[3] Asmussen S.,Kroese D. P. and Rubinstein R. Y. (2005).Heavy tails, importance sampling and cross-entropy.Stoch. Models 21,5776.
[4] Botev Z. I. and Kroese D. P. (2012).Efficient Monte Carlo simulation via the generalized splitting method.Statist. Comput. 22,116.
[5] Botev Z. I.,L'Ecuyer P. and Tuffin B. (2013).Markov chain importance sampling with applications to rare event probability estimation.Statist. Comput. 23,271285.
[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.183194.
[7] Dupuis P. Leder K. Wang H. (2007).Importance sampling for sums of random variables with regularly varying tails.ACM TOMACS 17,14.
[8] Embrechts P. and Goldie C. M. (1980).On closure and factorization properties of subexponential and related distributions.J. Austral. Math. Soc. A 29,243256.
[9] Embrechts P.,Kluppelberg C. and Mikosch T. (1997).Modelling Extremal Events.Springer,Berlin.
[10] Foss S.,Korshunov D. and Zachary S. (2011).An Introduction to Heavy-Tailed and Subexponential Distributions,Springer,New York.
[11] Ghamami S. and Ross S. M. (2012). Improving the Asmussen–Kroese-type simulation estimators.J. Appl. Prob. 49,11881193.
[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. 51,359376.
[13] Juneja S. (2007).Estimating tail probabilities of heavy tailed distributions with asymptotically zero relative error.Queueing Systems 57,115127.
[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. 77,5469.
[15] Wong R.(2001).Asymptotic Approximation of Integrals (Classics Appl. Math. 34).Society for Industrial and Applied Mathematics,Philidelphia, PA..
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Applied Probability
  • ISSN: 0021-9002
  • EISSN: 1475-6072
  • URL: /core/journals/journal-of-applied-probability
Please enter your name
Please enter a valid email address
Who would you like to send this to? *



Full text views

Total number of HTML views: 0
Total number of PDF views: 46 *
Loading metrics...

Abstract views

Total abstract views: 151 *
Loading metrics...

* Views captured on Cambridge Core between 24th October 2016 - 15th December 2017. This data will be updated every 24 hours.