kenberg, on 2014-February-03, 12:39, said:
OK, I see we can also get confidence intervals. We are speaking here of confidence that this average sample median will be close to the actual median of the original sample, is that right? Say the original sample, of 100,000 in my formulation, comes from a population of 100,000,000. A confidence interval that refers back to this 100,000,000 population would be really great. But it seems like we would need some strobg assumptions to get this. Or not?But presumably the median for the 100,000 is of some decent resemblance to the median for the whole population.
I don't have MATLAB up and running right now so I can't run a controlled experiment. However, if I used a decent size for the bootstrap (say 1K samples for simple stuff), the difference between the mean of the bootstrap medians and the population median was usually "epsilon" (too small to worry about). The confidence intervals should be as accurate.
With respect to your question about sample size:
In general, if you're doing statistical sampling you get to assume asymptoptic normality.
A sample size of 100,000 is lovely, but is probably severe overkill unless you expect something weird with the original population.