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I have an experimental sample, size of about 1000 values​​. I need to generate a much larger sample for simulation. I can create a samples like this:

library(ks)
x<-rlnorm(1000)
y<-rkde(fhat=kde(x=x, h=hpi(x)), n=10000, positive = TRUE)#
z<-sample(x, 10000, replace = TRUE)

par(mfrow=c(3,1))
hist(x, freq=F, breaks=100,  col="red")
hist(y, freq=F, breaks=100,  col="green")
hist(z, freq=F, breaks=100,  col="blue")

What fundamental limitations when using KDE or bootstrap? How else can I create such a sample?

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    $\begingroup$ Please, don't cross-post on multiple sites. $\endgroup$ – chl Apr 21 '13 at 8:30
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With the KDE you are smoothing your data to get guess what the distribution is. Then you are sampling from that distribution.

With bootstrapping, you are resampling from the data that you already have.

One difference between the two methods is that KDE can result in values that you did not observe in your original sample. In bootstrap this cannot happen. Whether this is good or bad depends on what you know about this distribution. If you think your sample already represents well the distribution, bootstrapping might be better.

A third approach might be to look at the histogram or use some prior knowledge about the distribution to fit some parametric distribution.

You have to understand though, that there are general limitations to what you are trying to do. In general, unless you have some prior beliefs about your distribution, you will not be able to "discover" a phenomenon that you did not observe in your sample by generating a larger sample artificially in this manner.

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    $\begingroup$ Thank you! You may suggest other ways to create big sample with properties experimental sample? $\endgroup$ – Andy Apr 20 '13 at 22:17

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