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Robust linear regression with broad distributions of errors

Author

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  • Postnikov, Eugene B.
  • Sokolov, Igor M.

Abstract

We consider the problem of linear fitting of noisy data in the case of broad (say α-stable) distributions of random impacts (“noise”), which can lack even the first moment. This situation, common in statistical physics of small systems, in Earth sciences, in network science or in econophysics, does not allow for application of conventional Gaussian maximum-likelihood estimators resulting in usual least-squares fits. Such fits lead to large deviations of fitted parameters from their true values due to the presence of outliers. The approaches discussed here aim onto the minimization of the width of the distribution of residua. The corresponding width of the distribution can either be defined via the interquantile distance of the corresponding distributions or via the scale parameter in its characteristic function. The methods provide the robust regression even in the case of short samples with large outliers, and are equivalent to the normal least squares fit for the Gaussian noises. Our discussion is illustrated by numerical examples.

Suggested Citation

  • Postnikov, Eugene B. & Sokolov, Igor M., 2015. "Robust linear regression with broad distributions of errors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 434(C), pages 257-267.
    • Handle: RePEc:eee:phsmap:v:434:y:2015:i:c:p:257-267
    DOI: 10.1016/j.physa.2015.04.025
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    References listed on IDEAS

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    1. Ursula Gather & Karen Schettlinger & Roland Fried, 2006. "Online signal extraction by robust linear regression," Computational Statistics, Springer, vol. 21(1), pages 33-51, March.
    2. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731, January.
    3. Gulich, Damián & Zunino, Luciano, 2014. "A criterion for the determination of optimal scaling ranges in DFA and MF-DFA," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 397(C), pages 17-30.
    4. Grech, Dariusz & Mazur, Zygmunt, 2013. "On the scaling ranges of detrended fluctuation analysis for long-term memory correlated short series of data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(10), pages 2384-2397.
    5. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
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    Cited by:

    1. Guus Balkema & Paul Embrechts, 2018. "Linear Regression for Heavy Tails," Risks, MDPI, vol. 6(3), pages 1-70, September.

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