Distribution Estimation Using Concomitants of Order Statistics, with Application to Monte Carlo Simulation for the Bootstrap
研究了Efron提出的近似自助法分布的模拟方法，证明其与顺序统计量伴随量技术相关，并分析了渐近性质，发现方差和均方误差随模拟次数和样本量下降，但尾部表现不如中心区域。
SUMMARY We show that a simulation method suggested by Efron for approximating bootstrap distributions is closely related to techniques based on concomitants of order statistics and develop its asymptotic properties from that viewpoint. We prove that the method produces Monte Carlo approximations with variance and mean-squared error decreasing like B− 1 n− 1/2, where B denotes the number of simulations and n equals the sample size. Therefore Efron's method can be a competitor with techniques such as balanced resampling, importance resampling and antithetic resampling, where variance and mean-squared error decrease like B −1 with no significant contribution from sample size. However, Efron's method has drawbacks, one being that performance in the tails is not as good as performance towards the centre of the distribution. In this respect, importance resampling has distinct advantages.