Doubly functional graphical models in high dimensions

Xinghao Qiao, Cheng Qian, Gareth M. James and Shaojun Guo

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

Abstract: We consider estimating a functional graphical model from multivariate functional observations. In functional data analysis, the classical assumption is that each function has been measured over a densely sampled grid. However, in practice the functions have often been observed, with measurement error, at a relatively small number of points. We propose a class of doubly functional graphical models to capture the evolving conditional dependence relationship among a large number of sparsely or densely sampled functions. Our approach first implements a nonparametric smoother to perform functional principal components analysis for each curve, then estimates a functional covariance matrix and finally computes sparse precision matrices, which in turn provide the doubly functional graphical model. We derive some novel concentration bounds, uniform convergence rates and model selection properties of our estimator for both sparsely and densely sampled functional data in the high-dimensional large-$p$, small-$n$ regime. We demonstrate via simulations that the proposed method significantly outperforms possible competitors. Our proposed method is applied to a brain imaging dataset.

Keywords: constrained `1-minimization; functional principal component; functional precision matrix; graphical model; high-dimensional data; sparesely sampled functional data (search for similar items in EconPapers)
JEL-codes: C1 (search for similar items in EconPapers)
Pages: 17 pages
Date: 2020-06-01
New Economics Papers: this item is included in nep-ecm and nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Published in Biometrika, 1, June, 2020, 107(2), pp. 415 - 431. ISSN: 0006-3444

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Persistent link: https://EconPapers.repec.org/RePEc:ehl:lserod:103120

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