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Monte Carlo likelihood inference in multivariate model-based geostatistics

Author

Listed:
  • Marco Minozzo

    () (Department of Economics (University of Verona))

  • Clarissa Ferrari

    () (Department of Economics (University of Verona))

Abstract

Though in the last decade many works have appeared in the literature dealing with model-based extensions of the classical (univariate) geostatistical mapping methodology based on linear Kriging, very few authors have concentrated, mainly for the inferential problems they pose, on model-based extensions of classical multivariate geostatistical techniques like the linear model of coregionalization, or the related `factorial kriging analysis'. Nevertheless, in presence of multivariate spatial non-Gaussian data, in particular count data, as in many environmental applications, the use of these classical techniques can lead to incorrect predictions about the underling factors. To overcome this problem, here we discuss a hierarchical geostatistical factor model that extends, following a model-based geostatistical approach, the classical geostatistical proportional covariance model. For this model we investigated likelihood-based inferential procedures based on the Monte Carlo EM algorithm and on Monte Carlo likelihood. In particular, we discuss some of their theoretical properties and report some simulation studies performed to investigate their sampling distributions.

Suggested Citation

  • Marco Minozzo & Clarissa Ferrari, 2012. "Monte Carlo likelihood inference in multivariate model-based geostatistics," Working Papers 33/2012, University of Verona, Department of Economics.
  • Handle: RePEc:ver:wpaper:33/2012
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    References listed on IDEAS

    as
    1. Marco Minozzo, 2011. "On the existence of some skew normal stationary processes," Working Papers 20/2011, University of Verona, Department of Economics.
    2. J. Zhu & J. C. Eickhoff & P. Yan, 2005. "Generalized Linear Latent Variable Models for Repeated Measures of Spatially Correlated Multivariate Data," Biometrics, The International Biometric Society, vol. 61(3), pages 674-683, September.
    3. Adelchi Azzalini, 2005. "The Skew‚Äźnormal Distribution and Related Multivariate Families," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(2), pages 159-188, June.
    4. Marco Minozzo & Clarissa Ferrari, 2013. "Multivariate geostatistical mapping of radioactive contamination in the Maddalena Archipelago (Sardinia, Italy): spatial special issue," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 97(2), pages 195-213, April.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Cokriging; generalized linear mixed models; linear model of coregionalization; Monte Carlo EM; spatial factor model; spatial prediction;

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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