Penalized Functional Principal Components Analysis
Using a Kullback-Leibler Criterion
University of Pennsylvania
Biostatistics/Statistics Joint Faculty Candidate
Wednesday, February 28, 2007, 12:00-1:00
In this talk, I propose a new data driven penalized method for performing functional principal components analysis. The penalty is based on a regularity of the underlying covariance function that is characterized by the balance between the decays of the eigenvalues and smoothness of the eigenfunctions. I propose to use the Kullback-Leibler distance to directly measure the goodness-of-fit in the space of functional covariances. A leave-one-trajectory-out cross validation procedure is introduced to estimate this Kullback-Leibler distance that allows for the selection of the smoothing parameter and the number of principal components.
Asymptotic consistency rates are computed which show that procedures selecting smoothing parameters based on metrics over the space of subject trajectories behave sub-optimally. Simulation studies are presented to demonstrate the method's empirical properties, while its practical relevance is illustrated through the analysis of time-course gene expression of the temporal transcriptional response of human fibroblast to serum.
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