A Latent Variable Approach to Modelling Multivariate Geostatistical Skew-Normal Data

Bagnato, Luca; Minozzo, Marco

doi:10.1007/10104_2014_14

Cited by 5 publications

(4 citation statements)

References 28 publications

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“…This article puts forward and discusses a model for the analysis of skewed multivariate geostatistical data, which shares the same building strategy of Bagnato and Minozzo (2014). Whereas in this latter work they prove that the finite‐dimensional marginal distributions of the multivariate spatial process are closed skew normal, here we prove that they are SUN.…”

Section: Discussionmentioning

confidence: 99%

“…Let us note that Bagnato and Minozzo (2014), without giving any explicit expression, prove that (5) has a multivariate closed skew-normal distribution (Gonzalez-Farias et al, 2004), that is, that all finite-dimensional marginal distributions of the process are closed skew-normal. However, though this is an interesting theoretical result, it suffers from the overparametrization of the closed skew normal (see Arellano-Valle & Azzalini, 2006).…”

Section: Probabilistic Propertiesmentioning

confidence: 99%

“…Note that this estimation procedure extends the MCEM procedure given in Bagnato and Minozzo (2014), which is implemented only for some of the parameters, assuming as completely known the spatial autocorrelation function and the skewness parameters.…”

Section: Parameter Estimationmentioning

confidence: 99%

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A unified skew‐normal geostatistical factor model

Minozzo

Bagnato

2021

Environmetrics

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The classical linear model of coregionalization and its simpler counterpart known as the proportional covariance model, or intrinsic correlation model, have become standard tools in many areas of application for the analysis of multivariate spatial data. Despite the merits of this model, it guarantees optimal predictions only in the case of Gaussian data and can lead to erroneous conclusions in all other circumstances, in particular in the presence of skew data. To deal with multivariate geostatistical data showing some degree of skewness, this article proposes a latent spatial factor model in which all finite‐dimensional marginal distributions are multivariate unified skew‐normal. For this model, we can write the log‐likelihood function of the data and implement a maximum likelihood estimation procedure which enables the simultaneous estimation of all parameters of the model. Moreover, we also show how the computational burden involved in the nonlinear mapping of the latent factors can be substantially reduced by exploiting a linearity property of the predictions. The sampling performances of the inferential procedures are investigated in some thorough simulation studies, and an application to radioactive contamination data is presented to show the flexibility of the model. Detailed derivations of our results are available as Supplementary Material.

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Section: Discussionmentioning

confidence: 99%

Section: Probabilistic Propertiesmentioning

confidence: 99%

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A unified skew‐normal geostatistical factor model

Minozzo

Bagnato

2021

Environmetrics

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“…Furthermore, skew-normality should be tested after applying the method on the factors. Recently, Bagnato & Minozzo (2014) proposed a spatial latent factor model to deal with multivariate geostatistical skew-normal data. In this model they assume that the unobserved latent structure, responsible for the correlation among different variables as well as for the spatial autocorrelation among different sites is normal, and that the observed variables are skew-normal.…”

Section: Introductionmentioning

confidence: 99%

Skewed factor models using selection mechanisms

Kim

Maadooliat

Arellano–Valle

et al. 2016

Journal of Multivariate Analysis

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Please cite this article as: H.-M. Kim, M. Maadooliat, R.B. Arellano-Valle, M.G. Genton, Skewed factor models using selection mechanisms, Journal of Multivariate Analysis (2015), http://dx.doi.org/10.1016/j.jmva. 2015.12.007 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Skewed Factor Models using Selection MechanismsHyoung Abstract Traditional factor models explicitly or implicitly assume that the factors follow a multivariate normal distribution; that is, only moments up to order two are involved. However, it may happen in real data problems that the first two moments cannot explain the factors. Based on this motivation, here we devise three new skewed factor models, the skew-normal, the skewt, and the generalized skew-normal factor models depending on a selection mechanism on the factors. The ECME algorithms are adopted to estimate related parameters for statistical inference. Monte Carlo simulations validate our new models and we demonstrate the need for skewed factor models using the classic open/closed book exam scores dataset.

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Bayesian hierarchical robust factor analysis models for partially observed sample-selection data

Kim

2018

Journal of Multivariate Analysis

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A Latent Variable Approach to Modelling Multivariate Geostatistical Skew-Normal Data

Cited by 5 publications

References 28 publications

A unified skew‐normal geostatistical factor model

A unified skew‐normal geostatistical factor model

Skewed factor models using selection mechanisms

Bayesian hierarchical robust factor analysis models for partially observed sample-selection data

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