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Activity Number: 548
Type: Contributed
Date/Time: Wednesday, August 7, 2013 : 10:30 AM to 12:20 PM
Sponsor: Section on Nonparametric Statistics
Abstract - #310353
Title: Representing Derivatives and Inferring Empirical Dynamics for Longitudinal Data
Author(s): Wenwen Tao*+ and Hans-Georg G. Müller
Companies: UC davis and University of California, Davis
Keywords: functional data analysis ; local polynomial methods ; functional principal component analysis ; stochastic differential equation
Abstract:

We propose a novel nonparametric approach to model and explicitly represent the derivatives for longitudinal data. Only assuming the underlying stochastic process is second order differentiable, our methods recover the derivatives by recovering each component in their Karhunen-Lo\`eve representation, which is shown to be a parsimonious and the most efficient representation for derivatives. Without directly observing the derivative processes, we start by functional data analysis on the trajectories, which can lead to the recovery of the covariance structure for the derivative processes. From there the components in Karhunen-Lo\`eve representation of the derivatives can be obtained and the derivatives are recovered. This approach is designed for irregularly spaced and sparsely observed cases, but also works satisfactorily on densely observed cases. Consistency and asymptotic convergence rate of the estimation are proved under certain mild conditions. The proposed methods are illustrated with an application on the BLSA data as an irregular, sparse example, and Fly daily volatility data as a dense example.


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