Functional Convex Averaging and Synchronization for
TimeWarped Random Curves

HansGeorg Muller
UC Davis
Monday, 4 October 2004
4:10 PM
E202, Engineering
ABSTRACT
Functional data for dynamic phenomena may be timewarped. It is then often inadequate to use commonly employed sample statistics such as the crosssectional mean or the crosssectional sample variance. If one observes trajectories that exhibit random transformations of the time scale, one may consider subjecting each observed curve to a time transformation in an attempt to reverse the warping of the time scale. For this purpose, we propose a functional convex synchronization model, under the premise that each observed curve is the realization of a stochastic process. Monotonicity constraints on time evolution provide the motivation to develop a functional convex calculus. Observed random functions in warped time space are represented by a bivariate random function in synchronized time space. This leads to the definition of a functional convex average. We discuss various implementations of functional convex averaging and derive a functional limit theorem and asymptotic confidence intervals for functional convex means. In a second part, we discuss the implementation of a simple timeshift warping method and its application to gene expression profiles. This talk is based on joint work with Xueli Liu and Xiaoyan Leng.
Refreshments will be served at 3:45 p.m. in Room 008 of the Statistics Building