Penalized analysis of correlated functional data
The aim of this dissertation is to create a unified and practical approach to the analysis of correlated functional data where realizations of a stochastic process over a space of smooth functions are observed at discreet observation points with noise. A philosophy for the penalized estimation of the second moment of the stochastic process is introduced by using the common smoothness of the underlying subject trajectories to induce a measure of regularity over the space of covariance functions. By showing that the amount of smoothing for covariance estimation is different than the amount of smoothing required for trajectory estimation, this dissertation offers some of the first in-depth discussions about practical smoothing parameter selection for second moment estimation. Further, a Kullback-Leibler criterion based on a metric over the space of covariance functions is offered for the selection of smoothing parameters. This framework is used to develop explicit techniques for performing functional principal components analysis (FPCA), efficient functional regression, and functional classification analysis. The time-course expression of human fibroblast to growth serum is analyzed through a FPCA that takes the spectral decomposition of the covariance estimator while using the Kullback-Leibler criterion to jointly select the smoothing parameter and number of principal components. A procedure for fitting the varying-coefficient model when the within-subject correlation is unknown is developed by iterating between weighted penalized least squares estimation of functional coefficients conditional on the covariance and the covariance estimation procedure conditional on functional coefficients. This approach to functional linear regression is used to investigate the clinical role that VEGF plays in the interaction of chemotherapy and antiangiogenic therapy. Finally, a quadratic rule for the classification of populations of locally stationary time series that takes into account within-population spectral variability is developed from smooth estimates of the mean and covariance of the log-spectra and used for the prediction of epileptic seizures from intracranial EEG data.
|Year of publication:||
|Authors:||Krafty, Robert Todd|
|Type of publication:||Other|
Dissertations available from ProQuest
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