Simultaneous Inference for Eigensystems and FPC Scores of Functional Data

Statistical Seminar

Organizer：

吴宇楠

Speaker：

胡祺睿

清华大学统计学研究中心

Time：

Mon., 11:00-12:00

Dec. 16, 2024

Venue：

C548, Shuangqing Complex Building A

Online：

Zoom Meeting ID: 271 534 5558

Passcode: YMSC

Title：

Simultaneous Inference for Eigensystems and FPC Scores of Functional Data

Abstract：

Functional data analysis has become a pivotal field in statistics, emphasizing data represented by functions rather than scalar values. Although significant progress has been made in estimating fundamental elements such as mean and covariance functions, simultaneous inference for eigensystems and functional principal component (FPC) scores remains challenging.

In this talk, we introduce novel methodologies for the simultaneous inference of eigensystems and the distribution of FPC scores in densely observed functional data, along with the asymptotic properties, especially holding in C[0,1] and for a diverging number of estimators. We validate our approaches through simulations and apply them to electroencephalogram (EEG) data, demonstrating their practical utility in testing hypotheses related to FPCs and the distribution of FPC scores. Finally, we discuss extensions to two-dimensional functional data, functional time series, and a the unified theory bridging sparse and dense functional data.