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Spatial Variability in Slash Linear Modeling with Finite Second Moment

Author

Listed:
  • R. S. Fagundes

    (Federal Technological University of Paraná)

  • M. A. Uribe-Opazo

    (Western Paraná State University)

  • M. Galea

    (Pontificia Universidad Católica de Chile)

  • L. P. C. Guedes

    (Western Paraná State University)

Abstract

This article studies the dependence of spatial linear models using a slash distribution with a finite second moment. The parameters of the model are estimated with maximum likelihood by using the EM algorithm. To avoid identifiability problems, the cross-validation, the Trace and the maximum log-likelihood value are used to choose the parameter for adjusting the kurtosis of the slash distribution and the selection of the model to explain the spatial dependence. We present diagnostic techniques of global and local influences for exploring the sensibility of estimators and the presence of possible influential observations. A simulation study is developed to determine the performance of the methodology. The results showed the effectiveness of the choice criteria of the parameter for adjusting the kurtosis and for the selection of the spatial dependence model. It has also showed that the slash distribution provides an increased robustness to the presence of influential observations. As an illustration, the proposed model and its diagnostics are used to analyze an aquifer data. The spatial prediction with and without the influential observations were compared. The results show that the contours of the interpolation maps and prediction standard error maps showed low changes when we removed the influential observations. Thus, this model is a robust alternative in the spatial linear modeling for dependent random variables. Supplementary materials accompanying this paper appear online.

Suggested Citation

  • R. S. Fagundes & M. A. Uribe-Opazo & M. Galea & L. P. C. Guedes, 2018. "Spatial Variability in Slash Linear Modeling with Finite Second Moment," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 23(2), pages 276-296, June.
    • Handle: RePEc:spr:jagbes:v:23:y:2018:i:2:d:10.1007_s13253-018-0322-0
    DOI: 10.1007/s13253-018-0322-0
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    References listed on IDEAS

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    1. Ann Mitchell, 1989. "The information matrix, skewness tensor and a-connections for the general multivariate elliptic distribution," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 41(2), pages 289-304, June.
    2. Miguel Angel Uribe-Opazo & Joelmir Andr� Borssoi & Manuel Galea, 2012. "Influence diagnostics in Gaussian spatial linear models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(3), pages 615-630, July.
    3. Osorio, Felipe & Paula, Gilberto A. & Galea, Manuel, 2009. "On estimation and influence diagnostics for the Grubbs' model under heavy-tailed distributions," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1249-1263, February.
    4. W.‐Y. Poon & Y. S. Poon, 1999. "Conformal normal curvature and assessment of local influence," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 51-61.
    5. Alcantara, Izabel Cristina & Cysneiros, Francisco José A., 2013. "Linear regression models with slash-elliptical errors," Computational Statistics & Data Analysis, Elsevier, vol. 64(C), pages 153-164.
    6. Zhang, Hao, 2004. "Inconsistent Estimation and Asymptotically Equal Interpolations in Model-Based Geostatistics," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 250-261, January.
    7. Manuel Galea & Jose Diaz-Garcia & Filidor Vilca, 2008. "Influence diagnostics in the capital asset pricing model under elliptical distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(2), pages 179-192.
    8. Fernanda De Bastiani & Audrey Mariz de Aquino Cysneiros & Miguel Uribe-Opazo & Manuel Galea, 2015. "Influence diagnostics in elliptical spatial linear models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(2), pages 322-340, June.
    9. R.A.B. Assumpção & M.A. Uribe-Opazo & M. Galea, 2014. "Analysis of local influence in geostatistics using Student's t -distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(11), pages 2323-2341, November.
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