Fast Covariance Estimation for Multivariate Sparse Functional Data

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...

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Bibliographic Details
Main Authors Li, Cai, Xiao, Luo, Luo, Sheng
Format Journal Article
LanguageEnglish
Published 02.12.2018
Subjects
Statistics - Computation
Statistics - Methodology
Online AccessGet full text
DOI10.48550/arxiv.1812.00538

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Summary: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.
DOI:10.48550/arxiv.1812.00538