a Key Laboratory of Advanced Theory and Application in Statistics, and Data Science – MOE, School of Statistics, East China Normal University, Shanghai, People's Republic of China
a Key Laboratory of Advanced Theory and Application in Statistics, and Data Science – MOE, School of Statistics, East China Normal University, Shanghai, People's Republic of China
a Key Laboratory of Advanced Theory and Application in Statistics, and Data Science – MOE, School of Statistics, East China Normal University, Shanghai, People's Republic of China
yczhou@stat.ecnu.edu.cn
b School of Data Science, Fudan University, Shanghai, People's Republic of China
xiaolei_xun@fudan.edu.cn
ABSTRACT
The unified weighing scheme for the local-linear smoother in analysing functional data can deal with data that are dense, sparse or of neither type. In this paper, we focus on the convergence rate of functional principal component analysis using this method. Almost sure asymptotic consistency and rates of convergence for the estimators of eigenvalues and eigenfunctions have been established. We also provide the convergence rate of the variance estimation of the measurement error. Based on the results, the number of observations within each curve can be of any rate relative to the sample size, which is consistent with the earlier conclusions about the asymptotic properties of the mean and covariance estimators.
Xingyu Yan, Yingchun Zhou, Xiaolong Pu, Peng Zhao. (2021) Functional Multiple-Outcome Model in Application to Multivariate Growth Curves of Infant Data. Journal of Systems Science and Complexity 24.
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Ziqi Chen, Jianhua Hu, Hongtu Zhu. (2020) Surface functional models. Journal of Multivariate Analysis 180, pages 104664.
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