Estimating a smooth covariance for functional data

Uche Mbaka, James Owen Ramsay and Michelle Carey

Computational Statistics & Data Analysis, 2026, vol. 213, issue C

Abstract: Functional data analysis frequently involves estimating a smooth covariance function based on observed data. This estimation is essential for understanding interactions among functions and constitutes a fundamental aspect of numerous advanced methodologies, including functional principal component analysis. Two approaches for estimating smooth covariance functions in the presence of measurement errors are introduced. The first method employs a low-rank approximation of the covariance matrix, while the second ensures positive definiteness via a Cholesky decomposition. Both approaches employ the use of penalized regression to produce smooth covariance estimates and have been validated through comprehensive simulation studies. The practical application of these methods is demonstrated through the examination of average weekly milk yields in dairy cows as well as egg-laying patterns of Mediterranean fruit flies.

Keywords: Functional data analysis; Spline smoothing; Matrix factorization; Cholesky decomposition; Covariance estimation; Positive definite; Low rank (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:213:y:2026:i:c:s0167947325001318

DOI: 10.1016/j.csda.2025.108255

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