A1240
Title: Scalable inference in functional linear regression with streaming data
Authors: Peijun Sang - University of Waterloo (Canada) [presenting]
Linglong Kong - University of Alberta (Canada)
Bei Jiang - University of Alberta (Canada)
Jinhan Xie - Yunnan University (China)
Enze Shi - University of Alberta (Canada)
Zuofeng Shang - New Jersey Institute of Technology (United States)
Abstract: Traditional static functional data analysis faces new challenges due to streaming data, where data constantly flows in. A major challenge is that storing such an ever-increasing amount of data in memory is nearly infeasible. In addition, existing inferential tools in online learning are mainly developed for finite-dimensional problems, while inference methods for functional data are focused on the offline setting. The focus is on the online estimation of functional linear regression with a scalar response and a functional covariate. To tackle these issues in this setting, a functional stochastic gradient descent algorithm is developed, and an online bootstrap resampling procedure is proposed that enables the performance of the {local (and global)} inference for the slope function in functional linear regression. In particular, the proposed estimation and inference procedures use only one pass over the data; thus, they are easy to implement and suitable for situations where data arrive in a streaming manner. Furthermore, the convergence rate and the asymptotic distribution are established for the proposed slope function estimator. The proposed perturbed estimator from the bootstrap procedure is shown to enjoy the same theoretical properties, which provide the theoretical justification for the online inference tool.
