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Influence diagnostics in elliptical spatial linear models

Author

Listed:
  • Fernanda De Bastiani
  • Audrey Mariz de Aquino Cysneiros
  • Miguel Uribe-Opazo
  • Manuel Galea

Abstract

In recent years, there has been a growing interest in statistical methods for the analysis of spatially referenced data. The spatial dependence structure modeling is an indispensable tool to estimate the parameters that define this structure. In this paper, we use the family of elliptical distributions to estimate the spatial dependence in referenced data. Thus we extend the Gaussian spatial linear model. Also we use the local influence methodology to assess the sensitivity of the maximum likelihood estimators to small perturbations in the data and/or in the spatial linear model assumptions. The methodology is illustrated with a real data set. The results allowed us to conclude that the presence of atypical values in the sample data have a strong influence, changing the spatial dependence structure. Also we have included a small simulation study. Copyright Sociedad de Estadística e Investigación Operativa 2015

Suggested Citation

  • 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.
    • Handle: RePEc:spr:testjl:v:24:y:2015:i:2:p:322-340
    DOI: 10.1007/s11749-014-0409-z
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    References listed on IDEAS

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    1. Manuel Galea & Gilberto Paula & Miguel Uribe-Opazo, 2003. "On influence diagnostic in univariate elliptical linear regression models," Statistical Papers, Springer, vol. 44(1), pages 23-45, January.
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    5. 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.
    6. Ibacache-Pulgar, Germán & Paula, Gilberto A., 2011. "Local influence for Student-t partially linear models," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1462-1478, March.
    7. Osorio, Felipe & Paula, Gilberto A. & Galea, Manuel, 2007. "Assessment of local influence in elliptical linear models with longitudinal structure," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4354-4368, May.
    8. Cambanis, Stamatis & Huang, Steel & Simons, Gordon, 1981. "On the theory of elliptically contoured distributions," Journal of Multivariate Analysis, Elsevier, vol. 11(3), pages 368-385, September.
    9. 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.
    10. Peter Filzmoser & Anne Ruiz-Gazen & Christine Thomas-Agnan, 2014. "Identification of local multivariate outliers," Statistical Papers, Springer, vol. 55(1), pages 29-47, February.
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    Cited by:

    1. Alejandra Tapia & Victor Leiva & Maria del Pilar Diaz & Viviana Giampaoli, 2019. "Influence diagnostics in mixed effects logistic regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(3), pages 920-942, September.
    2. Christian E. Galarza & Tsung-I Lin & Wan-Lun Wang & Víctor H. Lachos, 2021. "On moments of folded and truncated multivariate Student-t distributions based on recurrence relations," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(6), pages 825-850, August.
    3. Moreno Bevilacqua & Christian Caamaño‐Carrillo & Reinaldo B. Arellano‐Valle & Víctor Morales‐Oñate, 2021. "Non‐Gaussian geostatistical modeling using (skew) t processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(1), pages 212-245, March.
    4. Fidel Ernesto Castro Morales & Dimitris N. Politis & Jacek Leskow & Marina Silva Paez, 2022. "Student’s-t process with spatial deformation for spatio-temporal data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(5), pages 1099-1126, December.
    5. D. T. Nava & F. De Bastiani & M. A. Uribe-Opazo & O. Nicolis & M. Galea, 2017. "Local Influence for Spatially Correlated Binomial Data: An Application to the Spodoptera frugiperda Infestation in Corn," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 22(4), pages 540-561, December.
    6. Gustavo Henrique Dalposso & Miguel Angel Uribe-Opazo & Fernanda De Bastiani, 2021. "Spatial-temporal Analysis of Soybean Productivity Using Geostatistical Methods," Journal of Agricultural Studies, Macrothink Institute, vol. 9(2), pages 283-303, June.
    7. 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.

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