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摘要翻译：
重要性抽样是减少Monte Carlo估计方差的有力工具。基于参数族内Monte Carlo估计方差最小的准则，给出了求最优倾角测度的一般方法。为此，当底层分布的矩母函数存在时，我们得到了最优交替分布的一个简单而明确的表达式。该算法具有很好的通用性，适用于正态分布、非中心分布、复合泊松过程等。为了说明该方法的广泛适用性，我们研究了金融风险管理中的VaR计算和统计推断中的bootstrap置信域。
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英文标题：
《Efficient Importance Sampling for Rare Event Simulation with
Applications》
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作者：
Cheng-Der Fuh and Huei-Wen Teng and Ren-Her Wang
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最新提交年份：
2013
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分类信息：
一级分类：Statistics 统计学
二级分类：Methodology 方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
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一级分类：Quantitative Finance 数量金融学
二级分类：Risk Management 风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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英文摘要：
Importance sampling has been known as a powerful tool to reduce the variance of Monte Carlo estimator for rare event simulation. Based on the criterion of minimizing the variance of Monte Carlo estimator within a parametric family, we propose a general account for finding the optimal tilting measure. To this end, when the moment generating function of the underlying distribution exists, we obtain a simple and explicit expression of the optimal alternative distribution. The proposed algorithm is quite general to cover many interesting examples, such as normal distribution, noncentral $\chi^2$ distribution, and compound Poisson processes. To illustrate the broad applicability of our method, we study value-at-risk (VaR) computation in financial risk management and bootstrap confidence regions in statistical inferences.
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PDF链接：
https://arxiv.org/pdf/1302.0583
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