“数字+”与统计数据工程系列讲座（九十五）4月16日西南财经大学陈坤教授来中心讲座

讲座题目：

Spectral functional classification for time series with an application to epileptic seizure detection

主讲人： 陈坤

讲座时间：2025年4月16日（周三）  15:30

讲座地点：综合楼615会议室

主讲人简介：

陈坤，西南财经大学统计学院教授、博士生导师，光华英才学者，研究方向为时间序列分析、空间统计、函数型数据分析和金融统计。荣获光华优秀硕士学位论文指导教师。多次指导学生获得统计建模、市场调查、数学建模比赛国家级奖项。曾多次赴日本早稻田大学、日本北海道大学、台湾中研院、香港中文大学、香港城市大学、浙江大学和其他国内外多所高校访问。为香港城市大学统计学研究生开设课程。主持并参与了多项国家自然科学基金项目、教育部人文社科项目；在《Annals of Statistics》、《Statistica Sinica》、《Insurance: Mathematics and Economics》、《Journal of Time Series Analysis》、《统计研究》等国内外重要期刊发表论文； 是《Journal of the American Statistical Association》、《Statistica Sinica》、《Bernoulli》、《Journal of Time Series Analysis》等多个期刊的匿名审稿人。

讲座摘要：

Statistical diagnosis of epileptic seizures based on electroencephalogram (EEG) signals is often challenging to implement due to time dependency and possible existence of measurement errors. In this article, by reframing the seizure detection as a classification problem for stationary time series processes, we propose a novel frequency domain functional approach to simultaneously account for time dependency and noise reduction. The procedure is based on the spectral theory of time series and identifies series whose spectral density share similar shapes or oscillations. The main tool of our proposed method is smoothed logarithm of the periodogram, which serves as an asymptotically consistent estimator for the logarithm of the spectral density. In addition, by employing the functional principal component analysis (FPCA) combined with a distance-based rule, similarities and disparities between smoothed log-periodograms and thus log-spectral densities can be identified. Under mild regularity conditions, we theoretically demonstrate that the misclassification rates tend to zero. Based on extensive simulations in various scenarios and real applications to EEG data of epilepsy patients, the efficacy of our proposed method is demonstrated.