Title: Adjusting systematic bias in high dimensional principal component scores,
Abstract: Principal component analysis continues to be a powerful tool in dimension
reduction of high dimensional data. We assume a variance-diverging model and
use the high-dimension, low-sample-size asymptotics to show that even though
the principal component directions are not consistent, the sample and
prediction principal component scores can be useful in revealing the population
structure. We further show that these scores are biased, and the bias is
asymptotically decomposed into rotation and scaling parts. We propose methods
of bias-adjustment that are shown to be consistent and work well in the finite
but high dimensional situations with small sample sizes. The potential
advantage of bias-adjustment is demonstrated in a classification setting.