Function-on-Function Regression with Thousands of Predictive Curves
报告人： Ruiyan Luo, Georgia State University
时间：2017-05-25 14:00 ~ 15:00
地点：1114M, Science Building 1 (理科1号楼)
With the advance of technology, thousands of curves can be simultaneously recorded by electronic devices, such as the simultaneous EEG and fMRI data. To study the relationship between these curves, we consider a functional linear regression model with functional response and functional predictors, where the number of predictive curves is much larger than the sample size. The high dimensionality of this problem poses theoretical and practical difficulties for the existing methods, including estimation inconsistency and prediction inaccuracy. Motivated by the simultaneous EEG and fMRI data, we focus on models with sparsity structures where most of the coefficient functions of the predictive curves have small norms. To take advantage of this sparsity structure and the smoothness of coefficient functions, we propose a simultaneous sparse-smooth penalty which is incorporated into a generalized functional eigenvalue problem to obtain estimates of the model. We establish the asymptotic upper bounds for the prediction and estimation errors as both the sample size and the number of predictive curves go to infinity. Simulation studies show that the proposed method has good predictive performance for the models with sparsity structures. The proposed method is applied to a simultaneous EEG and fMRI dataset.
About the Speaker:
Dr. Ruiyan Luo is Associate Professor in the Division of Epidemiology and Biostatistics at the School of Public Health of Georgia State University. She received her B.S. in 2000 and M.S. in 2002 in Applied Mathematics from Tianjin University, and Ph.D. in Statistics from the University of Wisconsin-Madison in 2007. She did postdoctoral research in the Department of Epidemiology and Public Health at Yale University from 2007 to 2010. Her main research interests are functional data analysis, high dimensional data analysis, and Bayesian analysis. She has publications in journals such as JASA, Annals of Applied Statistics, and Journal of Computational and Graphical Statistics.