Confidence Intervals : The percentile method

As before we denote by the bootstrap distribution of , approximated by

The percentile method consists in taking the confidence interval for as being

Theoretically speaking this is equivalent to replacement of the unknown distribution by the estimate .

:

1. Input the level of the confidence interval
2. For b=1 to B do /* B is the number of bootstrap samples*/
3. For i=1 to n do /* Generation of Sample */
   1. OBS=RANINT(1,n)
   2. Add observation number OBS to the Sample
4. Compute
5. Combine the into a new data set THETA
6. Compute the and 'th quantiles for THETA.

An example of the implementation of this method in SAS and S for the correlation coefficient of the law-school data can be found in the Appendix .