A far-near sparse covariance model with application in climatology
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A far-near sparse covariance model with application in climatology Yi Li1
· Aidong Adam Ding2
Received: 29 July 2019 / Revised: 1 August 2020 / Accepted: 29 August 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract Teleconnection, the strong dependence between two distant locations, provides interesting information for discovering the structures in spatial data. While teleconnections are often sparse and estimated through sample correlations, there are also abundant correlations among nearby locations. We propose a far-near covariance model that simultaneously models the abundant short-distance dependencies and the sparse long-distance dependence. This approach provides a new framework for utilizing the short-distance dependence structure to improve the exploration and estimation of the sparse remote dependence signals. The statistical properties of proposed estimators are provided. The detection of teleconnection in high-dimensional data is a multiple testing problem. We relate this detection problem to τ -coherence statistical testing and generalize the τ -coherence for the covariance matrix of two-dimensional grid locations. The applications are illustrated through numerical studies on both synthetic data and real climate data. Keywords Climate · Covariance matrix · Teleconnection
1 Introduction In spatial statistics, the spatial covariance matrix is useful in both the supervised regression problem (Cressie 1993; Christensen 2002; Montero et al. 2015) and unsupervised problem (Benestad et al. 2015), as well as other areas such as spatial econometrics
Handling Editor: Pierre Dutilleul. Electronic supplementary material The online version of this article (https://doi.org/10.1007/s10651020-00462-4) contains supplementary material, which is available to authorized users.
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Yi Li [email protected]
1
MassMutual, 470 Atlantic Ave, Boston, MA, USA
2
Department of Mathematics, Northeastern University, Boston, MA, USA
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Environmental and Ecological Statistics
(LeSage and Pace 2009). Traditional spatial covariance models use some parametric form, such as the Matérn covariance, to model the covariance as a function of the spatial distance between locations. However, such spatial covariance models may not model enough complexity of the covariance in real data. Generally, the pairs of far-apart locations do not have the same dependence strength when the between distances are equal, as assumed in the covariance models such as the Matérn covariance. In climate studies, there exist strong correlations of some climate variables between certain distant locations (Grimm and Reason 2015; Cook et al. 2004). The sparse strong correlations between distant locations are called teleconnections and have been attracting interest in climate studies (Magrin et al. 2007; Tsonis et al. 2008; Choi et al. 2015). There is also recent interest using the teleconnections to build up climate networks (Donges et al. 2009; Steinhaeuser et al. 2010, 2011, 2012), which allows complex network analysis to
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