Statistics Seminar: STA 290
Sponsored by the Research Training Group of the Dept. of Statistics
Thursday, November 29th, 2012 at 4.10pm, MSB 1147 (Colloquium Room)
Refreshments 3:30pm, prior to seminar in MSB 4110 (Statistics Lounge)
Speaker: Victor Patrangenaru (Florida State University)
Title: Data Analysis on Sample Spaces with a Manifold Stratification
Abstract: Analysis of Object Data is the traditional name for Data Analysis on Sample Spaces with a Manifold Stratification. It includes multivariate analysis, directional data analysis, shape analysis, diffusion tensor imaging analysis, data analysis on Hilbert manifolds including functional data analysis, analysis of phylogenetic trees data; pretty much any non-categorical statistical problem can be formulated as object data analysis problem. Much of the standard nonparametric methodology extends from the multivariate case, in the generic case when the Frechet mean of a random object is a regular point of the sample space. Given a probability distribution on a stratified space, we define the concept of stickiness of the Frechet sample mean (Hotz et. al. (2012)). Motivated by a result due to Basrak(2010), our conjecture is that the limiting distribution of the Frechet sample mean is supported on the singular part of the sample space, and its tangential component to the singular part of the sample space at the population mean is multivariate normal.