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Spatial Outlier Accommodation Using a Spatial Variance Shift Outlier Model

Author

Listed:
  • Ali Mohammed Baba

    (Institute for Mathematical Research, Universiti Putra Malaysia, Serdang 43400, Selangor, Malaysia
    Department of Mathematical Sciences, Abubakar Tafawa Balewa University, Bauchi 0248, Nigeria)

  • Habshah Midi

    (Institute for Mathematical Research, Universiti Putra Malaysia, Serdang 43400, Selangor, Malaysia
    Department of Mathematics and Statistics, Faculty of Science, Universiti Putra Malaysia, Serdang 43400, Selangor, Malaysia)

  • Nur Haizum Abd Rahman

    (Institute for Mathematical Research, Universiti Putra Malaysia, Serdang 43400, Selangor, Malaysia
    Department of Mathematics and Statistics, Faculty of Science, Universiti Putra Malaysia, Serdang 43400, Selangor, Malaysia)

Abstract

Outlier detection has been a long-debated subject among researchers due to its effect on model fitting. Spatial outlier detection has received considerable attention in the recent past. On the other hand, outlier accommodation, particularly in spatial applications, retains vital information about the model. It is pertinent to develop a method that is capable of accommodating detected spatial outliers in a fashion that retains vital information in the spatial models. In this paper, we formulate the variance shift outlier model (SVSOM) in the spatial regression as a robust spatial model using restricted maximum likelihood (REML) and use weights based on the detected outliers in the model. The spatial outliers are accommodated via a revised model for the outlier observations with the help of the SVSOM. Simulation results show that the SVSOM, based on the detected spatial outliers is more efficient than the general spatial model (GSM). The findings of this study also reveal that contamination in the residuals and x variable have little effect on the parameter estimates of the SVSOM, and that outliers in the y variable are always detectable. Asymptotic distribution of the squared spatial prediction residuals are obtained to confirm the outlyingness of an observation. The merit of or proposed SVSOM for the detection and accommodating outliers is also confirmed using artificial and COVID-19 data sets.

Suggested Citation

  • Ali Mohammed Baba & Habshah Midi & Nur Haizum Abd Rahman, 2022. "Spatial Outlier Accommodation Using a Spatial Variance Shift Outlier Model," Mathematics, MDPI, vol. 10(17), pages 1-19, September.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:17:p:3182-:d:905831
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    References listed on IDEAS

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    1. Gumedze, Freedom N. & Welham, Sue J. & Gogel, Beverley J. & Thompson, Robin, 2010. "A variance shift model for detection of outliers in the linear mixed model," Computational Statistics & Data Analysis, Elsevier, vol. 54(9), pages 2128-2144, September.
    2. Rüdiger Lehmann & Michael Lösler & Frank Neitzel, 2020. "Mean Shift versus Variance Inflation Approach for Outlier Detection—A Comparative Study," Mathematics, MDPI, vol. 8(6), pages 1-21, June.
    3. Xiaowen Dai & Libin Jin & Anqi Shi & Lei Shi, 2016. "Outlier detection and accommodation in general spatial models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 25(3), pages 453-475, August.
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