Sample Size for Emperical CDF

From: Peter Michaux (petermichaux_at_yahoo.com)
Date: 09/30/04 

Date: 29 Sep 2004 21:58:06 -0700

I want to use the bootstrap to make confidence intervals for a
statistic. The quality of a bootstrap's output depends heavily on the
quality of the empirical cdf. If my sample is of size n, how big does
n have to be so that the empirical cdf is a good approximation of the
underlying cdf? I don't know anything about the underlying cdf.

I think the solution might be to watch the change in the empirical cdf
after I take each new sample. Eventually the empirical cdf won't be
changing that much after each new sample. At that point I can stop
sampling. Is this on the right track? I don't know how to quantify
that change and when the change in that quantity can be considered
small.

Thanks,
Peter