[R] Confidence intervals for PCA scores/eigenvalues

From: Markus Loecher <markus_at_insightfromdata.com>
Date: Fri, 01 Feb 2008 14:14:31 -0500


Very sorry about my incomplete email from 2 days ago, here is the full version.



Dear all,
I have read various descriptions of employing resampling techniques, such as the bootstrap, to estimate the uncertainties of the eigenvalues/vectors computed by PCA.
Let's say I define my test statistic T to be the percent of variance captured by the first 2 principal components. I am struggling with a conceptual issue here. Since PCA maximizes the variance concentration, wouldn't the bootstrapped distribution of T be biased upward due to the effectively reduced sample size ? If that is true, how could one obtain an unbiased confidence interval for T ?

Any insight would be helpful !

Thanks,

Markus



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