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Robust methods for the analysis of spatially autocorrelated data

Author

Listed:
  • Andrea Cerioli

    (Università di Parma)

  • Marco Riani

    (Università di Parma)

Abstract

In this paper we propose a new robust technique for the analysis of spatial data through simultaneous autoregressive (SAR) models, which extends the Forward Search approach of Cerioli and Riani (1999) and Atkinson and Riani (2000). Our algorithm starts from a subset of outlier-free observations and then selects additional observations according to their degree of agreement with the postulated model. A number of useful diagnostics which are monitored along the search help to identify masked spatial outliers and high leverage sites. In contrast to other robust techniques, our method is particularly suited for the analysis of complex multidimensional systems since each step is performed through statistically and computationally efficient procedures, such as maximum likelihood. The main contribution of this paper is the development of joint robust estimation of both trend and autocorrelation parameters in spatial linear models. For this purpose we suggest a novel definition of the elemental sets of the Forward Search, which relies on blocks of contiguous spatial locations.

Suggested Citation

  • Andrea Cerioli & Marco Riani, 2002. "Robust methods for the analysis of spatially autocorrelated data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 11(3), pages 335-358, October.
    • Handle: RePEc:spr:stmapp:v:11:y:2002:i:3:d:10.1007_bf02509831
    DOI: 10.1007/BF02509831
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    References listed on IDEAS

    as
    1. Andrea Cerioli, 2002. "Testing Mutual Independence Between Two Discrete-Valued Spatial Processes: A Correction to Pearson Chi-Squared," Biometrics, The International Biometric Society, vol. 58(4), pages 888-897, December.
    2. Lowe, Antony & Ridgway, Keith & Atkinson, Helen, 2000. "QFD in new production technology evaluation," International Journal of Production Economics, Elsevier, vol. 67(2), pages 103-112, September.
    3. R. Kelley Pace & James P. LeSage, 2004. "Spatial Statistics and Real Estate," The Journal of Real Estate Finance and Economics, Springer, vol. 29(2), pages 147-148, September.
    4. John Haslett & Kevin Hayes, 1998. "Residuals for the linear model with general covariance structure," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(1), pages 201-215.
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    Citations

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    Cited by:

    1. Francesca Torti & Aldo Corbellini & Anthony C. Atkinson, 2021. "fsdaSAS: A Package for Robust Regression for Very Large Datasets Including the Batch Forward Search," Stats, MDPI, vol. 4(2), pages 1-21, April.
    2. Fabio Crosilla & Domenico Visintini & Francesco Sepic, 2007. "An automatic classification and robust segmentation procedure of spatial objects," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 15(3), pages 329-341, February.
    3. Lisa Crosato & Luigi Grossi, 2019. "Correcting outliers in GARCH models: a weighted forward approach," Statistical Papers, Springer, vol. 60(6), pages 1939-1970, December.
    4. Torti, Francesca & Corbellini, Aldo & Atkinson, Anthony C., 2021. "fsdaSAS: a package for robust regression for very large datasets including the batch forward search," LSE Research Online Documents on Economics 109895, London School of Economics and Political Science, LSE Library.
    5. Andrea Cerioli & Marco Riani & Anthony C. Atkinson & Aldo Corbellini, 2018. "Rejoinder to the discussion of “The power of monitoring: how to make the most of a contaminated multivariate sample”," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(4), pages 661-666, December.
    6. Fabio Crosilla & Domenico Visintini & Francesco Sepic, 2007. "An automatic classification and robust segmentation procedure of spatial objects," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 15(3), pages 329-341, February.

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