[Gretl-users] Re: Resample without replacement (Artur Tarassow)

On Sat, 21 Sep 2019, Sven Schreiber wrote: Thanks for the references. I found Linton/Maasoumi/Whang heavy going but I think I understand Politis & Romano OK (and since LMW are drawing on the latter maybe I understand them well enough for current purposes too). If so, it appears they're not doing random sampling, they're considering all contiguous sub-samples of a certain size. This is clear in section 1 of Politis & Romano where they're talking about "subsets of the data that retain the dependence structure of the data." They say: <quote> For example, if X_i,...,X_n represent n observations from a stationary time series, the statistic is recomputed over the n - b + 1 subsets of size b of the form {X_i, X_{i+1},...X_{i+b-1}}. </quote> Let n = 6 and b = 2, so n - b + 1 = 5. It's clear what 5 subsets they must be talking about: (1,2) (2,3) (3,4) (4,5) (5,6) There's nothing random here and it would be easy to generate such subsets in hansl without the help of any special function. Randomness might come in at a "meta" level if one wanted to select a random subset of the full set of such samples -- presumably, without replacement. That could be done easily using msample() on a vector of contiguous index values (just {1,2,3,4,5} for the toy case above). Given the selected indices, getting the samples would then be a simple deterministic calculation. Allin