# Re: [R] bootstrap resampling - simplified

From: Vokey, John <vokey_at_uleth.ca>
Date: Wed, 02 Mar 2011 11:05:01 -0700

On 2011-03-02, at 4:00 AM, r-help-request_at_r-project.org 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 conditions. Firstly, every resampled database should also include 20 observations. Secondly, when selecting a number from the above-mentioned 20 numbers, you can do this selection with replacement. The difficult part comes now: one number can be selected only maximum 5 times. In order to make this clear I show you a couple of examples. So the resampled databases might be 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 (1, 2, 3, 4), each selected - for the maximum possible - 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 (the maximum possible times), number 1 selected 4 times, the others selected less than 4 times.
>
> (3rd database) 1,1,2,2,3,3,4,4,9,9,9,10,10,13,10,9,3,9,2,1
> Number 9 chosen for the maximum possible 5 times, number 10, 3, 2, 1 chosen for 3 times, number 4 selected twice and number 13 selected only once.
>

> ...
>
> Anybody knows how to implement my "tricky" condition into one of the R functions - that one number can be selected only 5 times at most? 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

Laszlo,
Create a vector consisting of 5 of each number. Then, for each sample, scramble the order of the items in the vector, and select the first 20.

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-Dr. John R. Vokey

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