Adaptive functional thresholding for sparse covariance function estimation in high dimensions

Qin Fang, Shaojun Guo and Xinghao Qiao

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

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.

Keywords: binning; high-dimensional functional data; functional connectivity; functional sparsity; local linear smoothing; partially observed functional data (search for similar items in EconPapers)
JEL-codes: C1 (search for similar items in EconPapers)
Pages: 13 pages
Date: 2024-10-31
New Economics Papers: this item is included in nep-ecm and nep-mfd
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Citations: View citations in EconPapers (1)

Published in Journal of the American Statistical Association, 31, October, 2024, 119(546), pp. 1473 - 1485. ISSN: 0162-1459

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Persistent link: https://EconPapers.repec.org/RePEc:ehl:lserod:118700

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