报告题目：Online Estimation for Functional Data

报 告 人：北京大学 姚方教授

报告时间：2022年5月23日（周一）14:00-17:00

报告形式：线上，腾讯会议：428 490 756

摘要：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.

报告人简介：姚方，北京大学讲席教授、国家特聘专家、北大统计科学中心主任，数理统计学会（IMS）Fellow与理事会理事，美国统计学会（ASA）Fellow。2000年本科毕业于中国科技大学统计专业，2003获得加利福尼亚大学戴维斯分校统计学博士学位，曾任职于多伦多大学统计科学系长聘正教授。至今担任9个国际统计学核心期刊的主编或编委，包括《加拿大统计学期刊》主编，顶级期刊《Journal of the American Statistical Association》和《Annals of Statistics》的编委等。

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