Tail distribution of the maximum of correlated Gaussian random variables
Tail distribution of the maximum of correlated Gaussian random variables
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相关高斯随机变量最大值的尾部分布
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
Ad Ridder
中科院分区：
文献类型：
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作者：
Z. Botev;M. Mandjes;Ad Ridder
本文考虑相关正态随机变量最大值尾分布的有效估计。我们发现，目前推荐的Monte Carlo估计有困难，在量化其精度，因为它的样本方差估计是一个低效的估计的真实方差。我们提出了一个简单的补救措施：仍然使用这个估计，但依赖于其精度的替代量化。此外，我们还考虑了一个全新的序贯重要性抽样估计所需的尾部概率。数值实验表明，序贯重要性抽样估计可以显着更有效地比它的竞争对手。
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.