Online Estimation for Functional Data
Date: Thursday, 7 April 2022
Time: 11 am - 12 noon
Functional data analysis has attracted considerable interest, and is facing new challenges of the increasingly available data in streaming manner. In this work, we propose a new online method to dynamically update the local linear estimates of mean and covariance functions of functional data, which is the foundation of subsequent analysis. The kernel-type estimates can be decomposed into two sufficient statistics depending on the data-driven bandwidths. We propose to approximate the future optimal bandwidths by a dynamic sequence of candidates and combine the corresponding statistics across blocks to make an updated estimation. The proposed online method is easy to compute based on the stored sufficient statistics and current data block. Based on the asymptotic normality of the online mean and covariance function estimates, the relative efficiency in terms of integrated mean squared error is studied and a theoretical lower bound is obtained. This bound provides insight into the relationship between estimation accuracy and computational cost driven by the length of candidate bandwidth sequence that is pivotal in the online algorithm. Simulations and real data applications are provided to support such findings and show the advantages of the proposed method.
Zoom Link: Please contact Yanrong Yang (yanrong.yang@anu.edu.au) to obtain the zoom link for this seminar.