University of California Davis
Functional Data Analysis: Theory and Application
Functional data analysis has gained increasing importance in modern data analysis due to the improved capability to record and store a vast amount of data and advances in scientific computing. Plenty of approaches have been proposed that perform satisfactorily in theory and practice, but many interesting theoretical problems for traditional functional data remain unresolved. Moreover, very few methods can adequately handle the next generation functional data, such as fMRI data.
In this talk I will review some of my recent research on both traditional and next generation functional data. I will primarily focus on the unifying estimation and theory for the mean and covariance function estimation. The asymptotic results enable systematic partition of functional data into three types: non-dense, dense and ultra-dense, which completes the silhouette of functional data. We also give a comprehensive comparison between two widely used weighting schemes, which provides guidance in data application.
Next, I will briefly show my current work on functional connectivity for resting state fMRI data. We demonstrate the problems of the predominantly used Pearson Correlation, and propose a new connectivity measure, Integrated Correlation, which is both theoretically justified and numerically reliable. If time permits, I will give a brief introduction to a time-varying additive model which not only reduces the dimensionality but also captures the time-dynamic features of longitudinal data.
Sponsored by the Department of Mathematical Sciences
Host: Robert Serfling
Refreshments will be served in Room FO 2.610F 30 minutes before the talk begins.