Re: how to calculate this?
- From: "Reef Fish" <Large_Nassau_Gr0uper@xxxxxxxxx>
- Date: 14 Sep 2006 11:55:41 -0700
jiaojialin@xxxxxxxxx wrote:
the size of population is N,
the size of sample is M (M <= N),
the sample is done by sampling WITH replacement,
the question is:
how to calculate the percentage (in a certain confidence)
of population which will be left out of this sample?
Bootstrap is a RE-SAMPLING method, sampling from the
same (single) SAMPLE from a population.
In that respect, whatever is left out of the original population
will forever be left out!
With replacement, you are still resampling from the SAME M
sample values.
Now, if your question is meant to ask what portion of the
sample of size M will be left out in the resampling process,
then each fixed point of the SAMPLE will be left out of the
bootstrap sample with probability (1-1/M)^M.
As M --> infinity the proportion approaches exp(-1).
-- Reef Fish Bob.
For example, if the population size is 100,
do a bootstrap sample of size 100, what is
the percentage which will not be included
in the sample?
.
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