Control variates and importance sampling for efficient bootstrap simulations
Control variates and importance sampling for efficient bootstrap simulations
复制标题
DOI：
10.1007/bf00162526
复制
发表时间：
1996-06-01
影响因子：
2.2
通讯作者：
Hesterberg, T
中科院分区：
文献类型：
--
作者：
Hesterberg, T
重要性抽样和控制变量已分别用作估计自举尾部分位数和矩的方差减小技术。我们对每种方法进行了调整，使其同时适用于分位数和矩，并在模拟示例中组合方法以获得4到30的因子减少方差。我们对控制变量进行了两项创新——将控制变量解释为一种重新加权的方法，以及使用鞍点来实现控制变量；这种组合只需要线性鞍点，但适用于一般统计，并产生精度为n(-1/2)B（-1）阶的估计，其中n是样本量，B是自举样本量。讨论了对经典重要抽样的两种修正——加权平均估计和混合设计分布。这些修改使重要性采样具有鲁棒性，并允许从用于估计分位数的相同自举模拟中估计矩。
Importance sampling and control variates have been used as variance reduction techniques for estimating bootstrap tail quantiles and moments, respectively. We adapt each method to apply to both quantiles and moments, and combine the methods to obtain variance reductions by factors from 4 to 30 in simulation examples.We use two innovations in control variates-interpreting control variates as a re-weighting method, and the implementation of control variates using the saddlepoint; the combination requires only the linear saddlepoint but applies to general statistics, and produces estimates with accuracy of order n(-1/2)B(-1), where n is the sample size and B is the bootstrap sample size.We discuss two modifications to classical importance sampling-a weighted average estimate and a mixture design distribution. These modifications make importance sampling robust and allow moments to be estimated from the same bootstrap simulation used to estimate quantiles.