2021/02/01 by Rou Zhong, Shishi Liu, Zhong, Rou +5 · 1 citation
Computer Science · Mathematics · #Advanced Statistical Methods and Models #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #Methodology (stat.ME) #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.2102.00911
openalex publication_date 2021/02/01 · openalex created_date 2021/02/15 · openalex updated_date 2026/07/28
Functional principal component analysis is essential in functional data analysis, but the inferences will become unconvincing when some non-Gaussian characteristics occur, such as heavy tail and skewness. The focus of this paper is to develop a robust functional principal component analysis methodology in dealing with non-Gaussian longitudinal data, for which sparsity and irregularity along with non-negligible measurement errors must be considered. We introduce a Kendall's τ function whose particular properties make it a nice proxy for the covariance function in the eigenequation when handling non-Gaussian cases. Moreover, the estimation procedure is presented and the asymptotic theory is also established. We further demonstrate the superiority and robustness of our method through simulation studies and apply the method to the longitudinal CD4 cell count data in an AIDS study.