The dimple in Gneiting's spatial-temporal covariance model

Kent, John T.; Mohammadzadeh, Mohsen; Mosammam, Ali M.

doi:10.1093/biomet/asr006

Cited by 29 publications

(27 citation statements)

References 14 publications

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“…Such covariances can also be adapted, by Yadrenko (1983)'s principle, to chordal distance in the spatial component. In the same spirit, we show the validity of a new class, that we call modified Gneiting class, obtained with the same plugging technique as in Gneiting (2002), but where the temporal component does not rescale the spatial distance, which overcomes the dimple problem (Kent et al, 2011).…”

Section: Introductionmentioning

confidence: 66%

Spatio-Temporal Covariance and Cross-Covariance Functions of the Great Circle Distance on a Sphere

Porcu¹,

Bevilacqua²,

Genton³

2016

Journal of the American Statistical Association

148

183

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In this paper, we propose stationary covariance functions for processes that evolve temporally over a sphere, as well as cross-covariance functions for multivariate random fields defined over a sphere. For such processes, the great circle distance is the natural metric that should be used in order to describe spatial dependence. Given the mathematical difficulties for the construction of covariance functions for processes defined over spheres cross time, approximations of the state of nature have been proposed in the literature by using the Euclidean (based on map projections) and the chordal distances. We present several methods of construction based on the great circle distance and provide closed-form expressions for both spatio-temporal and multivariate cases. A simulation study assesses the discrepancy between the great circle distance, chordal distance and Euclidean distance based on a map projection both in terms of estimation and prediction in a space-time and a bivariate spatial setting, where the space is in this case the Earth. We revisit the analysis of Total Ozone Mapping Spectrometer (TOMS) data and investigate differences in terms of estimation and prediction between the aforementioned distance-based approaches. Both simulation and real data highlight sensible differences in terms of estimation of the spatial scale parameter. As far as prediction is concerned, the differences can be appreciated only when the interpoint distances are large, as demonstrated by an illustrative example.

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Section: Introductionmentioning

confidence: 66%

Spatio-Temporal Covariance and Cross-Covariance Functions of the Great Circle Distance on a Sphere

Porcu¹,

Bevilacqua²,

Genton³

2016

Journal of the American Statistical Association

148

183

View full text Add to dashboard Cite

show abstract

“…For details, we refer to Gneiting (2002) and to the recent article Kent et al (2011). The authors of the latter article point out that in certain circumstances, covariances defined by Gneiting (2002) possess a counter-intuitive dimple, and in some cases, the magnitude of the dimple can be non-trivial.…”

Section: Non-separable Class Of Covariances and The Estimationmentioning

confidence: 99%

A Frequency Domain Approach for the Estimation of Parameters of Spatio‐temporal Stationary Random Processes

Rao

Das

Boshnakov

2014

Journal Time Series Analysis

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In this paper we consider the estimation of the parameters of the spatio-temporal covariances of spatio-temporal stationary random processes. We define Finite Fourier Transforms of the processes at each location and based on joint distribution of these complex valued random variables we define an approximate likelihood function and consider the maximization. Ideas are similar to Whittle likelihood function considered in time series. The sampling properties of the estimators are investigated. The method is applied to simulated data and also to pacific wind speed data considered earlier by Cressie and Huang [6].

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“…t ′ = t , is r 𝒟 (0) ≈ 3/ϕ X which is the spatial range of the exponential covariance function [see 22, Chapter 2]. We note the recent work of Kent et al [23] who pointed out a “dimple” property associated with (19). The dimple property was unknown to us at the time this work was done.…”

Section: Specifying the Smoothing Kernelmentioning

confidence: 89%

Kernel averaged predictors for spatio-temporal regression models

Heaton

Gelfand

2012

Spatial Statistics

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In applications where covariates and responses are observed across space and time, a common goal is to quantify the effect of a change in the covariates on the response while adequately accounting for the spatio-temporal structure of the observations. The most common approach for building such a model is to confine the relationship between a covariate and response variable to a single spatio-temporal location. However, oftentimes the relationship between the response and predictors may extend across space and time. In other words, the response may be affected by levels of predictors in spatio-temporal proximity to the response location. Here, a flexible modeling framework is proposed to capture such spatial and temporal lagged effects between a predictor and a response. Specifically, kernel functions are used to weight a spatio-temporal covariate surface in a regression model for the response. The kernels are assumed to be parametric and non-stationary with the data informing the parameter values of the kernel. The methodology is illustrated on simulated data as well as a physical data set of ozone concentrations to be explained by temperature.

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The dimple in Gneiting's spatial-temporal covariance model

Abstract: Gneiting (2002) proposed a nonseparable covariance model for spatial-temporal data. In present paper we show that in certain circumstances his model possesses a counterintuitive "dimple", which detracts from its modelling appeal.

Cited by 29 publications

References 14 publications

Spatio-Temporal Covariance and Cross-Covariance Functions of the Great Circle Distance on a Sphere

Spatio-Temporal Covariance and Cross-Covariance Functions of the Great Circle Distance on a Sphere

A Frequency Domain Approach for the Estimation of Parameters of Spatio‐temporal Stationary Random Processes

Kernel averaged predictors for spatio-temporal regression models

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