方法对比

	双重（迭代）自助法	贝叶斯自助法（Bayesian Bootstrap，由 Rubin 提出）	Bootstrap Inference
领域	统计学	统计学	统计学
方法族	Regression model	Regression model	Regression model
起源年份	1986	1981	1979
提出者	Hall (1986); Beran (1987)	Rubin (1981); large-sample theory by Lo (1987)	Bradley Efron
类型	Resampling calibration (nested bootstrap)	Resampling / posterior simulation	Resampling-based inference
开创性文献	Hall, P. (1986). On the Bootstrap and Confidence Intervals. Annals of Statistics, 14(4), 1431-1452.	Rubin, D. B. (1981). The Bayesian Bootstrap. The Annals of Statistics, 9(1), 130-134.	Efron, B. (1979). Bootstrap Methods: Another Look at the Jackknife. Annals of Statistics, 7(1), 1-26.
别名	iterated bootstrap, nested bootstrap, calibrated bootstrap, Çift Bootstrap (Double / Iterated Bootstrap)	Bayesian Bootstrap (Rubin), Rubin bootstrap, Dirichlet-weighted bootstrap	bootstrap, bootstrap resampling, nonparametric bootstrap, Bootstrap Çıkarımı
相关	5	5	5
摘要	The double bootstrap is a resampling method that calibrates a bootstrap confidence interval with a second, nested layer of bootstrap to bring its actual coverage closer to the nominal level. Introduced by Hall (1986) and Beran (1987), it is especially valuable for small samples and skewed distributions where a single-layer bootstrap under-covers.	The Bayesian Bootstrap, introduced by Donald B. Rubin in 1981, is a resampling method that produces a Bayesian counterpart to the frequentist bootstrap by assigning each observation a random weight drawn from a Dirichlet distribution. It yields a full posterior distribution for a statistic and allows prior information to be incorporated.	Bootstrap inference, introduced by Bradley Efron in 1979, estimates the sampling distribution of a statistic by repeatedly resampling the observed data with replacement. It requires no distributional assumption and produces reliable confidence intervals even in small samples.