Topics in Functional Data Analysis

University of Minnesota Ph.D. dissertation. June 2017. Major: Statistics. Advisor: Snigdhansu Chatterjee. 1 computer file (PDF); ix, 207 pages.It is common for modern applications to collect data continuously from a process over a time period. Such data sets can be conceptualized as a collection of continuous functions and termed as functional data. In this work, we first briefly review a hierarchical Bayesian model for application in medical imaging data. We then consider the problem of statistical learning from functional data using a proposed semi metric based on envelopes. We also discuss a multiple hypothesis testing approach based on bootstrap distribution of the p values. We demonstrate the application of our methods on climate data relating to Arctic Oscillations