Re: sample size vs. principal component analysis (PCA)

On 1/26/2006 1:18 PM, Roy wrote: 
Hi,

I was wondering whether there is any work been done on the following
topic.

How sample size of the data affect the accuracy of PCA?
Or, to put it another way, if the data is chosen from some
distribution, when the sample size decreases/increases, how much
difference between the eigenvalues and eigenvectors of the sample
covariance matrix and those of the true covariance?

I believe that larger sample sizes improve the PRECISION of the estimates from a PCA, but I don't think that a large sample size changes the accuracy of the estimates. I am not aware of such a study, and I think the answer would depend very much on the separation of the eignevalues of the true underlying distribution -- if there are eigenvalues that are "close together", a large sample size will be needed to estimate these eigenvalues precisely and if they are far apart, then a small sample size may be sufficient for your purposes.

--
Paige Miller
pmiller5@xxxxxxxxxxxxxxxx

It's nothing until I call it -- Bill Klem, NL Umpire
If you get the choice to sit it out or dance,
  I hope you dance -- Lee Ann Womack
.

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