The Problem of Dimensionality in Stratified Sampling
研究分层抽样在高维样本空间中难以应用的问题，提出一种利用影子响应变量降低维度的基本抽样方案，并通过两个实例展示相比原始蒙特卡洛方法可减少10%至90%的方差。
Stratified sampling is perhaps the most natural of the variance reduction techniques. However its use is often frustrated by the high dimensionality of the sample space. This paper investigates the difficulty and suggests a basic sampling scheme for use in such problems. The accuracy of estimators when this method of sampling is used is examined in detail. A way of implementing the scheme in practice is suggested which makes use of shadow response variables (variables which have similar properties to control variables). This reduces the dimensionality of the sample space to a tractable size. Two detailed examples are given for which a 10% to 90% reduction in variance is obtained compared with crude Monte Carlo.