统计与数据科学系系列学术报告之三百九十六-三百九十七

统计与数据科学系系列学术报告之三百九十六

时    间：2023年05月18日（周四）15:30-16:30

主持人：复旦大学 管理学院 统计与数据科学系 朱仲义教授

地    点：史带楼603室

报 告人：姚方 教授   北京大学

题    目：Theory of Functional PCA for noisy and discretely observed data

摘    要：Functional data analysis is an important research field in statistics which treats  data as random functions drawn from some infinite-dimensional functional space, and functional principal component analysis (FPCA) plays a central role for data reduction and representation. After nearly three decades of research, there remains a key problem unsolved, namely,  the perturbation analysis of covariance operator for diverging number of eigencomponents obtained from noisy and discretely observed data. This is fundamental for studying models and methods based on FPCA, while there has not been much progress since the result obtained by Hall et al. (2006) for a fixed number of eigenfunction estimates. In this work, we establish a unified theory for this problem, deriving the moment bounds of eigenfunctions and asymptotic distributions of eigenvalues for a wide range of sampling schemes. We also exploit double truncation to derive the uniform convergence of such estimated eigenfunctions. The technical arguments in this work are useful for handling the perturbation series of discretely observed functional data and can be applied in models and methods involving inverse using FPCA as regularization, such as functional linear regression.

个人简介：姚方，国家高层次人才，北京大学讲席教授，北大统计科学中心主任、概率统计系主任，数理统计学会与美国统计学会会士。2000年本科毕业于中国科学技术大学，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主编或编委，包括《加拿大统计学期刊》主编、顶级期刊《北美统计学会会刊》和 《统计年刊》的编委。

统计与数据科学系系列学术报告之三百九十七

时    间：2023年05月18日（周四）16:30-17:30

主持人：复旦大学 管理学院 统计与数据科学系 黎德元教授

地    点：史带楼603室

报 告人：王学钦 教授  中国科学技术大学

题    目：Dynamical regime changes

摘    要：With the proliferation of data throughout many fields comes the challenge of detecting abrupt changes in time series that feature complex measured variables that may not be Euclidean in nature. We introduce a method for consistently estimating the number of change-points and identifying their locations in time series that are valued in Metric spaces. We further demonstrate that the estimated change points converge at an optimal rate of O_P (1/T). Analysis of a real dataset and extensive simulations show that our method outperforms state-of-the-art methods, particularly when data are non-Euclidean or covariance structures vary over time.

个人简介：王学钦，中国科学技术大学管理学院讲席教授，2003年毕业于纽约州立大学宾汉姆顿分校，教育部高层次人才入选者。现担任教育部高等学校统计学类专业教学指导委员会委员、中国现场统计研究会副理事长、中国现场统计研究会教育统计与管理分会理事长、统计学国际期刊JASA等的Associate Editor、高等教育出版社Lecture Notes: Data Science, Statistics and Probability系列丛书的副主编。

 统计与数据科学系

2023-5-6