Fast covariance estimation for multivariate sparse functional data

Abstract

Covariance estimation is essential yet underdeveloped for analysing 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.

Document Details

Document Type
Pub Defense Publication
Publication Date
Jan 01, 2020
Source ID
10.1002/sta4.245

Entities

People

  • Cai Li
  • Luo Xiao
  • Sheng Luo

Organizations

  • Duke University
  • National Institute of Neurological Disorders and Stroke
  • National Institutes of Health
  • North Carolina State University
  • United States Department of Defense

Tags

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Linear Algebra
  • Statistical inference.