[R] Confidence intervals for PCA scores/eigenvalues

[Charles C. Berry]

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
>
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Charles C. Berry                            (858) 534-2098
                                             Dept of Family/Preventive Medicine
E mailto:cberry at tajo.ucsd.edu	            UC San Diego
http://famprevmed.ucsd.edu/faculty/cberry/  La Jolla, San Diego 92093-0901