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I am currently reading this article. In page 4, a resampling procedure is detailed:

To explore the effects of sample size on estimates of population mean and standard deviation, we sampled 42 black-tailed deer from a population in Monterey [...]. We calculated the mean and standard deviation for 1,000 randomly generated sub-samples from this data set, ranging in size from n=3 to n=41, and calculated mean values and standard errors on the mean for these parameters at each sample size for both [variables under study].

The authors conclude:

Standard errors on estimates of the standard deviation dropped to 0.01‰ at n=5. We set our minimum sample size at 5 individuals.

  1. The authors do not specify whether their resampling is made with or without replacement. What would be the good choice for this procedure to be valid?

  2. If this procedure is valid, how would it be called (and is it something usual)? Is it really bootstrap which is performed here? (I suppose that it depends from the answer to the previous question...)

Thanks!

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In regards to one, I think the fact that they only pick subsets of size 3 to 41 clearly implies that they do not use replacement, otherwise they subsets could just be of arbitrary size.

In terms of two, bootstrapping is generally with replacement since it is meant to simulate independent draws from the underlying population. If you have replacement you will have dependency between the draws. A few good answers relating to that is given here.

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