> On 8 Sep 2016, at 16:25, David L Carlson <dcarl...@tamu.edu> wrote:
>
> Sampling without replacement treats the sample as the population for the
> purposes of estimating the outcomes at smaller sample sizes. Sampling with
> replacement (the same as bootstrapping) treats the sample as one possible
> outcome of a larger population at that sample size.
But the resamples aren't actually independent samples from the underlying
population, and in contrast to the usual applications of bootstrapping they
don't give a good approximation of independent samples if you look at type
("species") counts.
In my understanding – which may be incomplete – bootstrapping works for a test
statistic computed from the measurements of a single numeric random variable
(or perhaps several r.v.) in an i.i.d. sample. The type count cannot be
expressed as such a test statistic, hence we get the underestimation bias from
sampling with replacement.
In NLP, we often use parametric power-law models of the population in order to
extrapolate type counts (e.g. using this implementation
http://zipfr.r-forge.r-project.org), but this implies strong (and often
inappropriate) assumptions about the population.
Best,
Stefan
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