# Fast Covariance Estimation for Multivariate Sparse Functional Data

arXiv: https://arxiv.org/abs/1812.00538 · HTML: https://mlsanity.com/paper/1812.00538/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Dec 2018.

## Built on by (most cited first, 1 of 1)

- [Efficient Multidimensional Functional Data Analysis Using Marginal Product Basis Systems](https://mlsanity.com/paper/2107.14728/) (2021)

## Abstract (arXiv)

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.