DOAJ Open Access 2020

Convergence rate of principal component analysis with local-linear smoother for functional data under a unified weighing scheme

Xingyu Yan Xiaolong Pu Yingchun Zhou Xiaolei Xun

Lihat Sumber DOI

Abstrak

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.

Topik & Kata Kunci

Probabilities. Mathematical statistics

Penulis (4)

Xingyu Yan

Xiaolong Pu

Yingchun Zhou

Xiaolei Xun

Format Sitasi

APA MLA BibTeX

Yan, X., Pu, X., Zhou, Y., Xun, X. (2020). Convergence rate of principal component analysis with local-linear smoother for functional data under a unified weighing scheme. https://doi.org/10.1080/24754269.2019.1656048

Akses Cepat

Lihat di Sumber doi.org/10.1080/24754269.2019.1656048

Informasi Jurnal

Tahun Terbit: 2020
Sumber Database: DOAJ
DOI: 10.1080/24754269.2019.1656048
Akses: Open Access ✓