Iterative Functional Principal
Component Analysis for Correlation Reduction
In this talk
we propose an iterative estimation procedure for performing functional
principal component analysis. The procedure aims at functional or
longitudinal data where the repeated measurements from the same subject
are correlated. For the handling of the
within-subject correlation, we develop an iterative procedure which
would gradually reduce the dependence amongst the repeated measurements
made for the same subject. An increasingly popular smoothing approach,
penalized spline regression, is used to represent the mean trend. This
allows straightforward incorporation of covariates and simple
implementation of inference procedures for coefficients. The resulting
data after iteration are theoretically shown to be asymptotically
independent, which suggests that the general theory of penalized spline
regression developed for independent data can also be applied to
functional data. The effectiveness of the
proposed procedure is demonstrated via a simulation study and an
application to yeast cell cycle data.