Tail distribution of the maximum of correlated Gaussian random variables

Zdravko I. Botev, Michel Mandjes, Ad Ridder

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Abstract

In this article we consider the efficient estimation of the tail distribution of the maximum of correlated normal random variables. We show that the currently recommended Monte Carlo estimator has difficulties in quantifying its precision, because its sample variance estimator is an inefficient estimator of the true variance. We propose a simple remedy: to still use this estimator, but to rely on an alternative quantification of its precision. In addition to this we also consider a completely new sequential importance sampling estimator of the desired tail probability. Numerical experiments suggest that the sequential importance sampling estimator can be significantly more efficient than its competitor.

Original languageEnglish
Title of host publication2015 Winter Simulation Conference, WSC 2015
PublisherInstitute of Electrical and Electronics Engineers, Inc.
Pages633-642
Number of pages10
Volume2016-February
ISBN (Electronic)9781467397438
DOIs
Publication statusPublished - 16 Feb 2016
EventWinter Simulation Conference, WSC 2015 - Huntington Beach, United States
Duration: 6 Dec 20159 Dec 2015

Conference

ConferenceWinter Simulation Conference, WSC 2015
CountryUnited States
CityHuntington Beach
Period6/12/159/12/15

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Botev, Z. I., Mandjes, M., & Ridder, A. (2016). Tail distribution of the maximum of correlated Gaussian random variables. In 2015 Winter Simulation Conference, WSC 2015 (Vol. 2016-February, pp. 633-642). [7408202] Institute of Electrical and Electronics Engineers, Inc.. https://doi.org/10.1109/WSC.2015.7408202