Instantaneous dynamics of functional data

Time dynamic systems can be used in many applications to data modeling. In the case of longitudinal data, the dynamics of the underlying differential equation can often be inferred under minimal assumptions via smoothing based procedures. This is in contrast to the common technique of assuming a prespecified differential equation, and estimating it's parameters. In many cases, one wants to learn the dynamics of a differential equation that incorporates more than just one stochastic process. In the following, we propose extensions to existing two-step smoothing methods that allow for the presence of additional functional data arising from a second stochastic process. We further introduce model comparison techniques to assess the hypothesis that there is a significant change in fit provided by this additional process. These techniques are applied to the instantaneous dynamics of mouse growth data and allow us to make comparisons between mice who have been assigned different genetic and physical conditions. Finally, to study the statistical properties of our proposed techniques, we carry out a simulation study based on the mouse growth data. Supplementary material : http://hdl.handle.net/2429/59574Science, Faculty ofStatistics, Department ofGraduat