[R] bootstrap resampling question

Tue Mar 1 19:18:20 CET 2011

I'm not sure that is equivalent to sampling with replacement, since if the 
first "draw" is 1, then the probability that the next draw will be one is 
4/100 instead of the 1/20 it would be in sampling with replacement. I 
think the way to do this would be what Greg suggested - something like:

bigsamp <- sample(1:20, 100, T)
idx <- sort(unlist(sapply(1:20, function(x) which(bigsamp == 
x)[1:5])))[1:20]
samp <- bigsamp[idx]

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r-help-bounces at r-project.org wrote on 03/01/2011 09:37:31 AM:

> [image removed] 
> 
> Re: [R] bootstrap resampling question
> 
> Giovanni Petris 
> 
> to:
> 
> Bodnar Laszlo EB_HU
> 
> 03/01/2011 11:58 AM
> 
> Sent by:
> 
> r-help-bounces at r-project.org
> 
> Cc:
> 
> "'r-help at r-project.org'"
> 
> A simple way of sampling with replacement from 1:20, with the additional
> constraint that each number can be selected at most five times is
> 
> > sample(rep(1:20, 5), 20)
> 
> HTH,
> Giovanni
> 
> On Tue, 2011-03-01 at 11:30 +0100, Bodnar Laszlo EB_HU wrote:
> > Hello there,
> > 
> > I have a problem concerning bootstrapping in R - especially 
> focusing on the resampling part of it. I try to sum it up in a 
> simplified way so that I would not confuse anybody.
> > 
> > I have a small database consisting of 20 observations (basically 
> numbers from 1 to 20, I mean: 1, 2, 3, 4, 5, ... 18, 19, 20).
> > 
> > I would like to resample this database many times for the 
> bootstrap process with the following two conditions. The resampled 
> databases should also have 20 observations and you can select each 
> of the previously mentioned 20 numbers with replacement. I guess it 
> is obvious so far. Now the more difficult second condition is that 
> one number can be selected only maximum 5 times. In order to make 
> this clear I try to show you an example. So there can be resampled 
> databases like the following ones:
> > 
> > (1st database)          1,2,1,2,1,2,1,2,1,2,3,3,3,3,3,4,4,4,4,4
> > (4 different numbers are chosen, each selected 5 times)
> > 
> > (2nd database)          1,8,8,6,8,8,8,2,3,4,5,6,6,6,6,7,19,1,1,1
> > (Two numbers - 8 and 6 - selected 5 times, number "1" selected 
> four times, the others selected less than 4 times)
> > 
> > My very first guess that came to my mind whilst thinking about the
> problem was the sample function where there are settings like 
> replace=TRUE and prob=... where you can create a probability vector 
> i.e. how much should be the probability of selecting a number. So I 
> tried to calculate probabilities first. I thought the problem can 
> basically described as a k-combination with repetitions. 
> Unfortunately the only thing I could calculate so far is the total 
> number of all possible selections which amounts to 137 846 527 049.
> > 
> > Anybody knows how to implement my second "tricky" condition into 
> one of the R functions? Are 'boot' and 'bootstrap' packages capable 
> of managing this? I guess they are, I just couldn't figure it out yet...
> > 
> > Thanks very much! Best regards,
> > Laszlo Bodnar
> > 
> > 
> 
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> -- 
> 
> Giovanni Petris  <GPetris at uark.edu>
> Associate Professor
> Department of Mathematical Sciences
> University of Arkansas - Fayetteville, AR 72701
> Ph: (479) 575-6324, 575-8630 (fax)
> http://definetti.uark.edu/~gpetris/
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