Empirical Dynamics for Longitudinal Data

• Activity Number: 272
• Type: Invited
• Date/Time: Tuesday, August 3, 2010 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Hans-Georg Mueller*+ and Fang Yao
• Companies: University of California, Davis and University of Toronto
• Keywords: Functional Data ; Derivatives ; Differential Equation ; Gaussian Process

Abstract

Derivatives of functions play an important role in assessing dynamics. Estimating derivatives from sparse, irregular and noisy measurements, as typically encountered in longitudinal studies, poses challenges. It is demonstrated how these can be overcome under minimal assumptions if one has a sample of random functions, each of which may be sparsely sampled. An application of derivative estimation is empirical dynamics, represented by an empirical stochastic differential equation that is constructed from the data and governs the smooth trajectories that generate the observations. This equation combines time-varying coefficients with a smooth drift process, and the relative contributions of the deterministic and stochastic components can be quantified. The interpretation of these components is of interest and is illustrated with longitudinal data.