On Fri, 1 Feb 2008, Markus Loecher wrote: > 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 ! >
See @article{beran1985bta, title={{Bootstrap Tests and Confidence Regions for Functions of a Covariance Matrix}}, author={Beran, R. and Srivastava, M.S.}, journal={The Annals of Statistics}, volume={13}, number={1}, pages={95--115}, year={1985}, publisher={JSTOR} } @article{beran1987cbt, title={{Correction: Bootstrap Tests and Confidence Regions for Functions of a Covariance Matrix}}, author={Beran, R. and Srivastava, M.S.}, journal={The Annals of Statistics}, volume={15}, number={1}, pages={470--471}, year={1987}, publisher={Institute of Mathematical Statistics} } and browse thru these perhaps: http://scholar.google.com/scholar?hl=en&lr=&&cites=1040478970084047991 HTH, Chuck > Thanks, > > Markus > > ______________________________________________ > R-help@r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. > Charles C. Berry (858) 534-2098 Dept of Family/Preventive Medicine E mailto:[EMAIL PROTECTED] UC San Diego http://famprevmed.ucsd.edu/faculty/cberry/ La Jolla, San Diego 92093-0901 ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.