Dan's Segment 23
These were done in class with Sean Trettel but using slightly different parameters. We used a Beta(2,3) distribution and our test statistic was an integral function of each draw. Our bootstrap estimate fluctuated between .54 and .58 with a standard deviation close to .15 or so, which is in line with the actual value of .56, computed analytically. Resampling the data from the Beta distribution did not provide a very different solution, so clearly the bootstrap method is working quite well here. The code used to perform these calculations can be found on Sean Trettel's wiki page.
To Think About
1. I think this would result in zero uncertainty (or close to it), since a sufficiently large resampling of the data would always result in the same minimum value. However, if you did not actually sample the population minimum in your initial data set, you will be getting an incorrect value for the minimum with nearly zero uncertainty, and this seems to violate the bootstrap theorem. However, I think the bootstrap theorem may only be that the distribution around the data value mimics the distribution around the population value, and in this case, both distributions would be nearly identical, they would just be around different values.