Robust Functional Principal Component Analysis for Non-Gaussian Longitudinal Data
| Autor: | Shishi Liu, Rou Zhong, Jingxiao Zhang, Haocheng Li |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Statistics and Probability
Functional principal component analysis FOS: Computer and information sciences Numerical Analysis Gaussian Inference Functional data analysis Function (mathematics) Asymptotic theory (statistics) Methodology (stat.ME) symbols.namesake Skewness Heavy-tailed distribution symbols Statistics Probability and Uncertainty Algorithm Statistics - Methodology Mathematics |
| DOI: | 10.48550/arxiv.2102.00911 |
| Popis: | 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 $\tau$ 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. |
| Databáze: | OpenAIRE |
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