Speaker: Daisuke Kurisu (Associate Professor, University of Tokyo, Japan)
Title: "Prediction, Inference, and Hypothesis Testing on non-Euclidean Data"
Abstract: In this talk, we discuss two topics on the statistical analysis of non-Euclidean data. First, we extend the notion of model averaging for conventional regression models to Frechet regression, which has Euclidean predictors and a non-Euclidean output. Specifically, we propose a cross-validation (CV) criterion to select model averaging weights and show its optimality in terms of the final prediction error. Simulation results demonstrate that the CV outperforms AIC- and BIC-type model averaging estimators. Second, we consider the problem of estimating the Frechet mean, which is a generalization of the conventional population mean. We develop an asymptotic theory of empirical likelihood (EL) methods for the estimation and inference of the generalized Frechet means of manifold-valued data. As a main result, we show that the EL statistics with an empirical Frechet mean converge in distribution to a chi-square distribution. We also discuss several extensions of the main result and illustrate our methods through real data analysis. My talk is based on joint works with Taisuke Otsu.
Faculty webpage (links to Google Site): https://sites.google.com/site/daisukekurisu/home
Seminar Date/Time: Thur, Oct 5, 4:10pm
Location: MSB 1147, Colloquium Room
Refreshments: 3:30pm, MSB 1147 Courtyard