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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 Kendalls $tau$ 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.
Functional principal component analysis (FPCA) could become invalid when data involve non-Gaussian features. Therefore, we aim to develop a general FPCA method to adapt to such non-Gaussian cases. A Kenalls $tau$ function, which possesses identical e
We propose a nonparametric method to explicitly model and represent the derivatives of smooth underlying trajectories for longitudinal data. This representation is based on a direct Karhunen--Lo`eve expansion of the unobserved derivatives and leads t
Functional principal component analysis (FPCA) has been widely used to capture major modes of variation and reduce dimensions in functional data analysis. However, standard FPCA based on the sample covariance estimator does not work well in the prese
Functional binary datasets occur frequently in real practice, whereas discrete characteristics of the data can bring challenges to model estimation. In this paper, we propose a sparse logistic functional principal component analysis (SLFPCA) method t
We consider spatially dependent functional data collected under a geostatistics setting, where locations are sampled from a spatial point process. The functional response is the sum of a spatially dependent functional effect and a spatially independe