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	置换 (随机化) 检验
领域	统计学	统计学	统计学	统计学
方法族	Regression model	Regression model	Regression model	Regression model
起源年份	1986	1981	1979	2005
提出者	Hall (1986); Beran (1987)	Rubin (1981); large-sample theory by Lo (1987)	Bradley Efron	Good (2005); Edgington & Onghena (2007); resampling tradition
类型	Resampling calibration (nested bootstrap)	Resampling / posterior simulation	Resampling-based inference	Nonparametric resampling test
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.	Good, P. (2005). Permutation, Parametric and Bootstrap Tests of Hypotheses (3rd ed.). Springer. ISBN: 978-0387202792
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	randomization test, exact permutation test, re-randomization test, Permütasyon Testi
相关	5	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.	The permutation test is a nonparametric resampling procedure that builds the sampling distribution of a test statistic directly from the data by repeatedly shuffling the group labels. Developed in the resampling tradition and treated systematically by Good (2005) and Edgington & Onghena (2007), it requires no parametric distributional assumption and yields an exact p-value.