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Longitudinal Functional Regression Models with Structured Penalties

Event Type
Statistics Department
165 Everitt
Mar 14, 2013   4:00 - 5:00 pm  
Jaroslaw (Jarek) Harezlak (Indiana University)

Collection of functional data has become more prevalent in the

past decade, including functional data collected longitudinally. For

example, in the HIV Neuroimaging Consortium (HIVNC) study, magnetic

resonance spectroscopy (MRS) was used to collect metabolite spectra from

multiple brain regions at a number of time points. Analysis of such data

usually follows a two-step procedure: (1) metabolite concentration

extraction and (2) association study of extracted covariates and outcomes

of interest.

Our approach does not rely on the frequently unreliable feature

extraction. Instead, it uses scientific knowledge to estimate regression

function without explicitly extracting the feature characteristics.

Specifically, we propose a method for functional linear model estimation

using partially empirical eigenvectors for regression (PEER) in the

longitudinal data setting. Our method allows the regression function to

vary across both time and space. We derive the estimator's statistical

properties and discuss their connections with the generalized singular

value decomposition (GSVD). The results of the simulation studies and an

application to the analysis of HIV patients' neurocognitive impairment as

a function of MRS data are presented.

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