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arXiv · 1812.00538

Fast Covariance Estimation for Multivariate Sparse Functional Data

Cai Li·Luo Xiao·Sheng Luo
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Abstract

Covariance estimation is essential yet underdeveloped for analyzing multivariate functional data. We propose a fast covariance estimation method for multivariate sparse functional data using bivariate penalized splines. The tensor-product B-spline formulation of the proposed method enables a simple spectral decomposition of the associated covariance operator and explicit expressions of the resulting eigenfunctions as linear combinations of B-spline bases, thereby dramatically facilitating subsequent principal component analysis. We derive a fast algorithm for selecting the smoothing parameters in covariance smoothing using leave-one-subject-out cross-validation. The method is evaluated with extensive numerical studies and applied to an Alzheimer's disease study with multiple longitudinal outcomes.

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Cai Li, Luo Xiao, Sheng Luo. 2018-12-03. Fast Covariance Estimation for Multivariate Sparse Functional Data. https://arxiv.org/abs/1812.00538

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