Covariance tapering for multivariate Gaussian random fields estimation

Bevilacqua, Moreno; Fassò, Alessandro; Gaetan, Carlo; Porcu, Emilio; Velandia, Daira

doi:10.1007/s10260-015-0338-3

Cited by 23 publications

(20 citation statements)

References 25 publications

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“…The lower bound provided by Theorem 5 is typically assumed in the references Shaby & Ruppert (2012), Bevilacqua et al (2015) and Furrer et al (2015).…”

Section: Proof Of Theoremmentioning

confidence: 99%

“…The picture is similar in the multivariate setting ( d > 1), but currently incomplete. The recent references Bevilacqua et al () and Furrer et al () provide asymptotic results for maximum likelihood approaches and require that the smallest eigenvalue of the covariance matrix of the observations be bounded away from zero as n → ∞ . However, this condition has currently only been shown to hold for some specific covariance functions and regular grids (Bevilacqua et al ).…”

Section: Introductionmentioning

confidence: 99%

“…1. However, this condition has currently only been shown to hold for some specific covariance functions and regular grids (Bevilacqua et al, 2015).…”

Section: Introductionmentioning

confidence: 99%

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On the smallest eigenvalues of covariance matrices of multivariate spatial processes

Bachoc

Furrer

2016

Stat

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There has been a growing interest in providing models for multivariate spatial processes. A majority of these models specify a parametric matrix covariance function. Based on observations, the parameters are estimated by maximum likelihood or variants thereof. While the asymptotic properties of maximum likelihood estimators for univariate spatial processes have been analyzed in detail, maximum likelihood estimators for multivariate spatial processes have not received their deserved attention yet. In this article we consider the classical increasing-domain asymptotic setting restricting the minimum distance between the locations. Then, one of the main components to be studied from a theoretical point of view is the asymptotic positive definiteness of the underlying covariance matrix. Based on very weak assumptions on the matrix covariance function we show that the smallest eigenvalue of the covariance matrix is asymptotically bounded away from zero. Several practical implications are discussed as well.

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“…The lower bound provided by Theorem 5 is typically assumed in the references Shaby & Ruppert (2012), Bevilacqua et al (2015) and Furrer et al (2015).…”

Section: Proof Of Theoremmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On the smallest eigenvalues of covariance matrices of multivariate spatial processes

Bachoc

Furrer

2016

Stat

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“…Unless the matrix is sparse or has a specific structure that eases the computation, O(N 3 ) floating points operations would be required for any matrix inversion. Approaches for modeling large covariance matrices in purely spatial settings include low rank and covariance tapering models [21,4,13, and references therein] and multivariate tapering proposed in Bevilacqua et al [7], approximations using Gaussian Markov Random Fields (GMRF), the Laplace transform and Stochastic Partial differential Equations [35,36,29,9,8], products of lower dimensional conditional densities [see 15,16, and references therein] and composite likelihoods [17] with the recent multivariate extension proposed in Bevilacqua et al [6]. A large number of extensions to spatio-temporal settings have been proposed, including [14], [20] and [27] who introduce dynamic spatio-temporal low-rank spatial processes, while [39] choose a GMRF approach.…”

Section: Spatio-temporal Interpolation Of Large Datasetsmentioning

confidence: 99%

A hierarchical multivariate spatio-temporal model for clustered climate data with annual cycles

Mastrantonio¹,

Lasinio²,

Pollice³

et al. 2019

Ann. Appl. Stat.

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We present a multivariate hierarchical space-time model to describe the joint series of monthly extreme temperatures and amounts of rainfall. Data are available for 360 monitoring stations over 60 years, with missing data affecting almost all series. Model components account for spatiotemporal dependence with annual cycles, dependence on covariates and between responses. The very large amount of data is tackled modeling the spatio-temporal dependence by the nearest neighbor Gaussian process. Response multivariate dependencies are described using the linear model of coregionalization, while annual cycles are assessed by a circular representation of time. The proposed approach allows imputation of missing values and easy interpolation of climate surfaces at the national level. The motivation behind is the characterization of the so called ecoregions over the Italian territory. Ecoregions delineate broad and discrete ecologically homogeneous areas of similar potential as regards the climate, physiography, hydrography, vegetation and wildlife, and provide a geographic framework for interpreting ecological processes, disturbance regimes, vegetation patterns and dynamics. To now, the two main Italian macro-ecoregions are hierarchically arranged into 35 zones. The current climatic characterization of Italian ecoregions is based on data and bioclimatic indices for the period 1955-1985 and requires an appropriate update.

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“…In particular, Bevilacqua et al (2015) consider estimation of the spatial covariance structure for a multivariate Gaussian random field using large datasets. To do this, they work with the so called two-taper tapering, which leads to unbiased estimation equations.…”

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confidence: 99%