Adaptive functional thresholding for sparse covariance function estimation in high dimensions

Fang, Qin, Guo, Shaojun and Qiao, Xinghao ORCID: 0000-0002-6546-6595 (2024) Adaptive functional thresholding for sparse covariance function estimation in high dimensions. Journal of the American Statistical Association, 119 (546). 1473 - 1485. ISSN 0162-1459

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Abstract

Covariance function estimation is a fundamental task in multivariate functional data analysis and arises in many applications. In this paper, we consider estimating sparse covariance functions for high-dimensional functional data, where the number of random functions p is comparable to, or even larger than the sample size n. Aided by the Hilbert–Schmidt norm of functions, we introduce a new class of functional thresholding operators that combine functional versions of thresholding and shrinkage, and propose the adaptive functional thresholding estimator by incorporating the variance effects of individual entries of the sample covariance function into functional thresholding. To handle the practical scenario where curves are partially observed with errors, we also develop a nonparametric smoothing approach to obtain the smoothed adaptive functional thresholding estimator and its binned implementation to accelerate the computation. We investigate the theoretical properties of our proposals when p grows exponentially with n under both fully and partially observed functional scenarios. Finally, we demonstrate that the proposed adaptive functional thresholding estimators significantly outperform the competitors through extensive simulations and the functional connectivity analysis of two neuroimaging datasets.

Item Type:	Article
Official URL:	https://www.tandfonline.com/journals/uasa20
Additional Information:	© 2023 The Authors
Divisions:	Statistics
Subjects:	H Social Sciences > HA Statistics
Date Deposited:	21 Apr 2023 11:18
Last Modified:	12 Dec 2024 03:42
URI:	http://eprints.lse.ac.uk/id/eprint/118700

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