Title: Functional Regression Modeling

Speaker: Hans-Georg M"uller, Department of Statistics, University
of California at Davis



ABSTRACT

Data in the form of functions or curves are increasingly common in the
sciences. We assume that per subject or unit one observes the realization
of a square integrable stochastic process, either as a response or as a
predictor. Our approach is via Karhunen-Loeve representations of these
processes in terms of the eigenfunctions of their covariance operator. For
special case where the processes are assumed Gaussian, we include the case
of sparse data where one does not observe the entire process, but only few
observations are available per subject, possibly contaminated with
measurement error.

Several aspects of regression modeling for such infinite-dimensional data
will be discussed. These include: Existence questions associated with the
"classical" functional linear model and functional least squares that
hinge on the existence of generalized inverses of compact operators in the
space of square integrable functions;  a representation of functional
least squares for the case of sparse data; and a proposed generalized
functional linear model. The latter may be useful for functional binomial
regression with applications in discrimination and classification. We
discuss an application to the classification of time-dynamic gene
expression data.  (Co-authors for the various parts include G. He, X.
Leng, U. Stadtm"uller, J.L. Wang and F. Yao).