Dear stats experts:
Me and my little brain must be missing something regarding bootstrapping. I
understand how to get a 95%CI and how to hypothesis test using bootstrapping
(e.g., reject or not the null). However, I'd also like to get a p-value from
it, and to me this seems simple, but it seems no-one does what I would like
to do to get a p-value, which suggests I'm not understanding something.
Rather, it seems that when people want a p-value using resampling methods,
they immediately jump to permutation testing (e.g., destroying dependencies
so as to create a null distribution). SO - here's my thought on getting a
p-value by bootstrapping. Could someone tell me what is wrong with my
approach? Thanks:

STEPS TO GETTING P-VALUES FROM BOOTSTRAPPING - PROBABLY WRONG:

1) sample B times with replacement, figure out theta* (your statistic of
interest). B is large (> 1000)

2) get the distribution of theta*

3) the mean of theta* is generally near your observed theta. In the same way
that we use non-centrality parameters in other situations, move the
distribution of theta* such that the distribution is centered around the
value corresponding to your null hypothesis (e.g., make the distribution
have a mean theta = 0)

4) Two methods for finding 2-tailed p-values (assuming here that your
observed theta is above the null value):
Method 1: find the percent of recentered theta*'s that are above your
observed theta. p-value = 2 * this percent
Method 2: find the percent of recentered theta*'s that are above the
absolute value of your observed value. This is your p-value.

So this seems simple. But I can't find people discussing this. So I'm
thinking I'm wrong. Could someone explain where I've gone wrong?


J Jackson

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