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Multiple Outlier Detection Tests for Parametric Models

Author

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  • Vilijandas Bagdonavičius

    (Institute of Applied Mathematics, Vilnius University, Naugarduko 24, LT-03225 Vilnius, Lithuania)

  • Linas Petkevičius

    (Institute of Computer Science, Vilnius University, Didlaukio 47, LT-08303 Vilnius, Lithuania)

Abstract

We propose a simple multiple outlier identification method for parametric location-scale and shape-scale models when the number of possible outliers is not specified. The method is based on a result giving asymptotic properties of extreme z -scores. Robust estimators of model parameters are used defining z-scores. An extensive simulation study was done for comparing of the proposed method with existing methods. For the normal family, the method is compared with the well known Davies-Gather, Rosner’s, Hawking’s and Bolshev’s multiple outlier identification methods. The choice of an upper limit for the number of possible outliers in case of Rosner’s test application is discussed. For other families, the proposed method is compared with a method generalizing Gather-Davies method. In most situations, the new method has the highest outlier identification power in terms of masking and swamping values. We also created R package outliersTests for proposed test.

Suggested Citation

  • Vilijandas Bagdonavičius & Linas Petkevičius, 2020. "Multiple Outlier Detection Tests for Parametric Models," Mathematics, MDPI, vol. 8(12), pages 1-23, December.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:12:p:2156-:d:455778
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    References listed on IDEAS

    as
    1. Douglas M. Hawkins, 1980. "Critical Values for Identifying Outliers," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 29(1), pages 95-96, March.
    2. S. Lalitha & Nirpeksh Kumar, 2012. "Multiple outlier test for upper outliers in an exponential sample," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(6), pages 1323-1330, November.
    3. A. C. Kimber, 1982. "Tests for Many Outliers in an Exponential Sample," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 31(3), pages 263-271, November.
    4. D. Kabe, 1970. "Testing outliers from an exponential population," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 15(1), pages 15-18, December.
    5. Lin, Chien-Tai & Balakrishnan, N., 2009. "Exact computation of the null distribution of a test for multiple outliers in an exponential sample," Computational Statistics & Data Analysis, Elsevier, vol. 53(9), pages 3281-3290, July.
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