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Activity Number: 421
Type: Topic Contributed
Date/Time: Tuesday, August 2, 2016 : 2:00 PM to 3:50 PM
Sponsor: Section on Nonparametric Statistics
Abstract #319743
Title: Optimal Designs for Longitudinal Studies via Functional Data Analysis
Author(s): Hao Ji* and Hans-Georg Mueller
Companies: University of California at Davis and University of California at Davis
Keywords: Asymptotics ; Coefficient of Determination ; Functional Principal Component ; Karhunen Loeve Expansion ; Sequential Optimization ; Sparse Design

How to optimally collect longitudinal data when the resources for data collection per subject are limited is of interest for designing longitudinal studies. For situations where one has underlying Gaussian processes with prior information about the underlying time-dynamic structure from a pilot study, we discuss optimal designs that are characterized by a few fixed time points where longitudinal predictor variables are to be measured. The proposed optimal designs are constructed for two specific settings. (a) Designs to recover the underlying smooth but unknown random trajectory curve for each subject, aiming to minimize squared prediction error. (b) Designs such that prediction errors for functional linear regression with functional/longitudinal predictors and scalar responses are minimized. Estimates of the proposed optimal longitudinal designs are shown to be consistent as the sample size of the pilot study increases. Sequential optimization is utilized to speed up selection procedures. The proposed designs are illustrated with simulations and data from the Baltimore Longitudinal Study of Aging.

Authors who are presenting talks have a * after their name.

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