bootstrap percentile confidence interval和bootstrap t confidence interval的比较
先说bootstrap percentile confidence interval的概念，它是指某统计量的bootstrap分布的2.5%和97.5%的间距。两种可信度区间的应用条件不一样，当bootstrap distribution近似符合正态分布，而且bias很小的时候，一般用t可信度区间，而如果不符合正态分布，但是bias很小时，只能够用bootstrap percentile 可信度区间。也就是说，用前者的时候不一定能够用后者，而能够用后者的时候肯定能够用前者。如果最终得到的两个区间不是很一致，则不推荐使用任何一种。
当上面两种可信度区间都不可用时，该用哪种可信度区间呢？下面是两种可以使用的可信度区间：BCa and tilting interval.
The bootstrap bias-corrected accelerated (BCa) interval is a modification of the percentile method that adjusts the percentiles to correct for bias and skewness.
The bootstrap tilting interval adjusts the process of randomly forming resamples (though a clever implementation allows use of the same resamples as other bootstrap methods).
The BCa method requires more than 1000 resamples for high accuracy. Use 5000 or more resamples if the accuracy of inference is very important. Tilting is more efficient, so that 1000 resamples are generally enough. Don’t forget that even BCa and tilting confidence intervals should be used cautiously when sample sizes are small, because there are not enough data to accurately determine the necessary corrections for bias and skewness.
参考自：Bootstrap Methods and Permutation Tests by Tim Hesterberg et al.
