# 对于bootstrap的一些粗浅认识

bootstrap就是从一个原始样本中进行有放回的重复采样，采样大小和原始样本大小相同，采样次数根据计算量而定。从每个重新样的样本中可以计算某个统计量的bootstrap 分布，比如说均值，多个重采样样本的均值构成了原始样本均值的bootstrap分布。在采样完后需要检查待研究统计量的bootstrap分布是不是符合正态分布。此外，统计量的bootstrap标准误等于该统计量bootstrap分布的标准差。

bootstrap分布与样本分布的比较

bias:the difference between the mean of its sampling distribution and the true value of the parameter；

bootstrap estimate of bias：the difference between themean of the bootstrap estimate of bias distribution and the value of the statistic in the original sample。Small bias means that the bootstrap distribution is centered at the statistic of the original sample and suggests that the sampling distribution of the statistic is centered at the population parameter.

Trimmed mean的含义：

A trimmed mean is the mean of only the center observations in a data set. In particular, the 25% trimmed mean x25% ignores the smallest 25% and the largest 25% of the observations. It is the mean of the

middle 50% of the observations.

bootstrap分布是否受到采样次数的影响？

bootstrap percentile confidence interval和bootstrap t confidence interval的比较

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.