Re: Sample Size for Emperical CDF

From: David Jones (dajxxx_at_ceh.ac.uk)
Date: 09/30/04 

Date: Thu, 30 Sep 2004 09:54:03 +0100

Peter Michaux wrote:
> 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.

 You can do something "in advance" by the usual simple argument ...
The empirical df at a given point is just a binomial random variable
divided by the sample size. The "probability of success" associated
with the binomial is derived from the true df at the point. Hence you
can get the variance of the empirical df in terms of the true df value
and the sample size. Then argue that if the true df is 0.95 say, and
you want to estimate it with a st.dev. of say 0.005 ... this then
gives the sample size required. This may not quite answer the actuall
question about accuracy of the confidence interval but it should give
a reasonable indication.

Relevant Pages

  • Re: Sample Size for Emperical CDF
    ... The quality of a bootstrap's output depends heavily on the ... > n have to be so that the empirical cdf is a good approximation of the ... the Kolmogorov quantile for a two sided interval is ...
    (sci.stat.math)
  • Sample Size for Emperical CDF
    ... The quality of a bootstrap's output depends heavily on the ... n have to be so that the empirical cdf is a good approximation of the ... I don't know anything about the underlying cdf. ... I don't know how to quantify ...
    (sci.stat.math)
Loading