Speaker: Hans-Georg Müller, Department of Statistics, University of

California, Davis

Title: Derivatives of Random Functions and Functional Gradients
 
Abstract
 
Derivatives of functions play an important role in assessing underlying
dynamics. Estimating derivatives from sparse, irregular and noisy
measurements as often encountered in longitudinal studies poses
challenges. It is demonstrated how these can be overcome under minimal
assumptions if one has a sparsely measured sample of random functions.
For Gaussian processes, one application of derivative estimation is a 
simple linear empirical differential equation that describes overall 
trends in the derivatives of the processes. As an example, we consider 
on-line auctions. A different and more complex kind of functional
derivative is of interest in the study of regression relations with a 
functional predictor and a scalar response. Here we aim at generalizing
nonparametric differentiation to the case where the argument is a 
function. Among various functional regression models, functional 
additive models emerge as a promising avenue. The resulting functional
gradient fields are illustrated for egg-laying curves of medflies. 
Joint work with Bitao Liu (Part 1) and Fang Yao (Part 2).