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Robust estimation for spatial autoregressive processes based on bounded innovation propagation representations

Author

Listed:
  • Grisel Maribel Britos

    (Universidad Nacional de Córdoba)

  • Silvia María Ojeda

    (Universidad Nacional de Córdoba)

Abstract

Robust methods have been a successful approach for dealing with contamination and noise in the context of spatial statistics and, in particular, in image processing. In this paper, we introduce a new robust method for spatial autoregressive models. Our method, called BMM-2D, relies on representing a two-dimensional autoregressive process with an auxiliary model to attenuate the effect of contamination (outliers). We compare the performance of our method with existing robust estimators and the least squares estimator via a comprehensive Monte Carlo simulation study, which considers different levels of replacement contamination and window sizes. The results show that the new estimator is superior to the other estimators, both in accuracy and precision. An application to image filtering highlights the findings and illustrates how the estimator works in practical applications.

Suggested Citation

  • Grisel Maribel Britos & Silvia María Ojeda, 2019. "Robust estimation for spatial autoregressive processes based on bounded innovation propagation representations," Computational Statistics, Springer, vol. 34(3), pages 1315-1335, September.
    • Handle: RePEc:spr:compst:v:34:y:2019:i:3:d:10.1007_s00180-018-0845-4
    DOI: 10.1007/s00180-018-0845-4
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    References listed on IDEAS

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    1. Raphael Gottardo & Adrian E. Raftery & Ka Yee Yeung & Roger E. Bumgarner, 2006. "Bayesian Robust Inference for Differential Gene Expression in Microarrays with Multiple Samples," Biometrics, The International Biometric Society, vol. 62(1), pages 10-18, March.
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    3. Baran, Sándor & Pap, Gyula & van Zuijlen, Martien C. A., 2004. "Asymptotic inference for a nearly unstable sequence of stationary spatial AR models," Statistics & Probability Letters, Elsevier, vol. 69(1), pages 53-61, August.
    4. Ojeda, Silvia & Vallejos, Ronny & Bustos, Oscar, 2010. "A new image segmentation algorithm with applications to image inpainting," Computational Statistics & Data Analysis, Elsevier, vol. 54(9), pages 2082-2093, September.
    5. Yao, Qiwei & Brockwell, Peter J, 2006. "Gaussian maximum likelihood estimation for ARMA models II: spatial processes," LSE Research Online Documents on Economics 5416, London School of Economics and Political Science, LSE Library.
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