Fast Covariance Estimation for Sparse Functional Data

TL;DR

This paper introduces a fast, spline-based covariance smoothing method tailored for sparse functional and longitudinal data, with demonstrated superior performance and practical applications in growth and health datasets.

Contribution

It presents a novel bivariate spline smoother for covariance estimation, along with an efficient algorithm using leave-one-subject-out cross validation.

Findings

Method outperforms existing covariance smoothing techniques.

Algorithm is computationally efficient for large datasets.

Successfully applied to child growth and CD4 count data.

Abstract

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.