# Fast Covariance Estimation for Sparse Functional Data

arXiv: https://arxiv.org/abs/1603.05758 · HTML: https://mlsanity.com/paper/1603.05758/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Mar 2016.

## Built on by (most cited first, 2 of 2)

- [Functional Generalized Canonical Correlation Analysis for studying multiple longitudinal variables](https://mlsanity.com/paper/2310.07330/) (2023)
- [Online Learning of Functional Principal Component Analysis for Multidimensional Functional Data](https://mlsanity.com/paper/2505.02131/) (2025)

## Abstract (arXiv)

Smoothing of noisy sample covariances is an important component in functional data analysis. We propose a novel covariance smoothing method based on penalized splines and associated software. The proposed method is a bivariate spline smoother that is designed for covariance smoothing and can be used for sparse functional or longitudinal data. We propose a fast algorithm for covariance smoothing using leave-one-subject-out cross validation. Our simulations show that the proposed method compares favorably against several commonly used methods. The method is applied to a study of child growth led by one of coauthors and to a public dataset of longitudinal CD4 counts.