Weighted composite likelihood-based tests for space-time separability of covariance functions

Bevilacqua, Moreno; Mateu, Jorge; Porcu, Emilio; Zhang, H.; Zini, Alessandro

doi:10.1007/s11222-009-9121-3

Cited by 15 publications

(10 citation statements)

References 38 publications

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“…A recent review in De Iaco, Posa, Cappello, and Maggio (2019) digs into other descriptive properties: Explicit distinction is made between partial, additive and total separability, as well as the concepts of axial, full and quadrant symmetries on the plane. Some tests on separability of space–time covariance functions can be found in Scaccia and Martin (2005, 2002, 2011), Fuentes (2006); Bevilacqua, Mateu, Porcu, Zhang, and Zini (2010), Mitchell, Genton, and Gumpertz (2006), Constantinou, Kokoszka, and Reimherr (2017), Lu and Zimmerman (2005), Aston, Pigoli, and Tavakoli (2017), Li et al (2007), De Iaco, Posa, & Myers, 2013, De Iaco, Palma, & Posa, 2016), and Cappello, De Iaco, and Posa (2018). Tests for axial symmetry are provided by Scaccia and Martin (2002, 2005).…”

Section: Properties Of Covariance Functionsmentioning

confidence: 99%

“…A recent space–time composite likelihood approach has been proposed by Bai, Song, and Raghunathan (2012). Finally, there have been also some work on tests based on composite likelihood (Bevilacqua et al, 2010). Computational aspects related to space–time covariance functions have been provided by De Cesare, Myers, and Posa (2002), De Iaco, Myers, Palma, and Posa (2010), and De Iaco and Posa (2012).…”

Section: Estimation Of Space–time Dependenciesmentioning

confidence: 99%

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30 Years of space–time covariance functions

Porcu

Furrer

Nychka

2020

WIREs Computational Stats

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In this article, we provide a comprehensive review of space–time covariance functions. As for the spatial domain, we focus on either the d‐dimensional Euclidean space or on the unit d‐dimensional sphere. We start by providing background information about (spatial) covariance functions and their properties along with different types of covariance functions. While we focus primarily on Gaussian processes, many of the results are independent of the underlying distribution, as the covariance only depends on second‐moment relationships. We discuss properties of space–time covariance functions along with the relevant results associated with spectral representations. Special attention is given to the Gneiting class of covariance functions, which has been especially popular in space–time geostatistical modeling. We then discuss some techniques that are useful for constructing new classes of space–time covariance functions. Separate treatment is reserved for spectral models, as well as to what are termed models with special features. We also discuss the problem of estimation of parametric classes of space–time covariance functions. An outlook concludes the paper. This article is categorized under: Statistical and Graphical Methods of Data Analysis > Analysis of High Dimensional Data Statistical Learning and Exploratory Methods of the Data Sciences > Modeling Methods Statistical and Graphical Methods of Data Analysis > Multivariate Analysis

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Section: Properties Of Covariance Functionsmentioning

confidence: 99%

Section: Estimation Of Space–time Dependenciesmentioning

confidence: 99%

30 Years of space–time covariance functions

Porcu

Furrer

Nychka

2020

WIREs Computational Stats

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“…This method involves more computation but is less prone to bias than subsampling, which is likely in finite samples to introduce extra bias with artificially created subsamples. Bevilacqua et al . (2010) adopted the parametric bootstrap approach for constructing tests of separability of space–time covariance functions.…”

Section: Simulation Experimentsmentioning

confidence: 99%

Joint Composite Estimating Functions in Spatiotemporal Models

Bai

Song

Raghunathan

2012

Journal of the Royal Statistical Society Series B: Statistical Methodology

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Modelling of spatiotemporal processes has received considerable attention in recent statistical research. However, owing to the high dimensionality of the data, the joint modelling of spatial and temporal processes presents a great computational challenge, in both likelihoodbased and Bayesian approaches. We propose a joint composite estimating function approach to estimating spatiotemporal covariance structures. This substantially reduces the computational complexity and is more efficient than existing composite likelihood methods. The novelty of the proposed joint composite estimating function is rooted in the construction of three sets of estimating functions from spatial, temporal and spatiotemporal cross-pairs, which results in overidentified estimating functions. Thus, we form a joint inference function in a spirit that is similar to Hansen's generalized method of moments. We show that under practical scenarios the estimator proposed is consistent and asymptotically normal. Simulation studies prove that our method performs well in finite samples. Finally, we illustrate the joint composite estimating function method by estimating the spatiotemporal dependence structure of airborne particulates (PM10) in the north-eastern USA over a 32-month period.

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“…Our aim is to find a set of weights W that yields the smallest possible value of tr[ Σ ( W )]. A similar idea was used in Bevilacqua et al (2009), who proposed minimizing the trace of a so-called Godambe information matrix in order to choose the value of a single tuning parameter in their composite likelihood estimation. Here, we consider the more complicated problem of choosing a potentially large number of weights w k : k = 1, …, K ; for example, in our Merseyside meningitis application, K = 4586.…”

Section: Choice Of Weightsmentioning

confidence: 99%

Estimating Individual-Level Risk in Spatial Epidemiology Using Spatially Aggregated Information on the Population at Risk

Diggle

Guan

Hart

et al. 2010

Journal of the American Statistical Association

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We propose a novel alternative to case-control sampling for the estimation of individual-level risk in spatial epidemiology. Our approach uses weighted estimating equations to estimate regression parameters in the intensity function of an inhomogeneous spatial point process, when information on risk-factors is available at the individual level for cases, but only at a spatially aggregated level for the population at risk. We develop data-driven methods to select the weights used in the estimating equations and show through simulation that the choice of weights can have a major impact on efficiency of estimation. We develop a formal test to detect non-Poisson behavior in the underlying point process and assess the performance of the test using simulations of Poisson and Poisson cluster point processes. We apply our methods to data on the spatial distribution of childhood meningococcal disease cases in Merseyside, U.K. between 1981 and 2007.

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Weighted composite likelihood-based tests for space-time separability of covariance functions

Cited by 15 publications

References 38 publications

30 Years of space–time covariance functions

30 Years of space–time covariance functions

Joint Composite Estimating Functions in Spatiotemporal Models

Estimating Individual-Level Risk in Spatial Epidemiology Using Spatially Aggregated Information on the Population at Risk

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