Bootstrapping data with only sampling weights given

Suppose you only have these information from a sample data: $X_i$ and $w_i$, $i=1,...,N$, where $w_i$'s are the respective sampling weights(not integers).

Is it possible to obtain a valid bootstrap estimate of say, variance of $X_i$?

I understand that I might have to readjust the sampling weights(for weighted data) for each bootstrap replicate to obtain a valid bootstrap estimate. But considering if I only have the above information, are there other ways to do this?

• There are several different meanings of "sampling weights"; for instance, Stata natively supports three different ones. Could you therefore explain what your weights mean? – whuber Feb 27 '14 at 17:05
• hi @whuber, in Stata it would be "pweights" – stats_newb Feb 28 '14 at 1:50
• My recollection is that these are probability weights: that is, you selected cases independently and randomly but with different chances of inclusion in the sample. Is that correct? – whuber Feb 28 '14 at 14:40
• Hi @whuber, these are weights that are calculated (with post-stratification applied) when sampling population and population of target inference are disparate. – stats_newb Mar 3 '14 at 8:24