2023/4/21 CRETA Seminar - Covariate adjusted functional principal component analysis

Title：

2023/4/21 CRETA Seminar - Covariate adjusted functional principal component analysis

Introduction：

Principal component analysis is a classical dimension reduction tool in multivariate statistical analysis and its extension to functional data, termed Functional Principal Component Analysis (FPCA), plays a central role in the analysis of samples that are curves, functions, or surfaces. When additional covariates are available, three major models could be considered to accommodate them into the framework of FPCA. The first model integrates the covariates in the mean function only, and the second model integrates them in both the mean and the covariance function. However, the first model is not suitable for data that display second-order variation, while the second model makes it difficult to perform subsequent statistical analyses on the dimension-reduced representations in addition to being time-consuming. The third model was proposed to tackle these issues. Specifically, it assumes the covariance function varies with the covariates via its eigenvalues while the corresponding eigenfunctions remain independent of the covariates. In addition to briefly introducing the proposed estimators for all three models, I will use different real examples to demonstrate their performance. 

About speaker：

Prof. Ci-Ren Jiang (Institute of Statistics and Data Science, National Taiwan University) 

Website: https://homepage.ntu.edu.tw/~cirenjiang/