[Gretl-users] Re: Resample without replacement (Artur Tarassow)
On Thu, 19 Sep 2019, Sven Schreiber wrote:
Am 19.09.2019 um 16:55 schrieb Riccardo (Jack) Lucchetti:
> On Thu, 19 Sep 2019, Allin Cottrell wrote:
>
> > As for the possibility of folding the without-replacement variant into
> > resample(), is the idea that without-replacement would also support
> > the blocksize option? (It would be easier if it didn't!)
>
> Unfortunately, it may do (I think: but it'd be nice if Stefano Fachin,
> our bootstrap guru, would give his opinion on the matter).
His opinion and examples of use cases would certainly be welcome. But
OTOH I think you're right, it's probably good to generalize this
properly now if it is touched at all.
On reflection it seems to me that sampling by blocks is conceptually
quite tricky in the without-replacement case. In a toy example,
suppose you have 10 observations and a blocksize of 3. The first
random selection takes, say, a block starting at t = 3. Now we can't
start a subsequent block at t = 1 or 2 because there won't be enough
contiguous observations. Each draw takes blocksize + p observations
out of the pool, where p is a random variable, so the max number of
draws we can make also becomes a random variable.
Or in this case would we take "without replacement" as applying to
blocks and not individual observations? (That is, it's OK to reuse
observations so long as all the blocks are unique.)
Allin