IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i12p2156-d455778.html
   My bibliography  Save this article

Multiple Outlier Detection Tests for Parametric Models

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/12/2156/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/12/2156/
    Download Restriction: no
    ---><---

    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. 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.
    3. 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.
    4. 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.
    5. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Nirpeksh Kumar, 2019. "Exact distributions of tests of outliers for exponential samples," Statistical Papers, Springer, vol. 60(6), pages 2031-2061, December.
    2. Chien-Tai Lin & Ying-Chen Lee & Narayanaswamy Balakrishnan, 2019. "Package mTEXO for testing the presence of outliers in exponential samples," Computational Statistics, Springer, vol. 34(2), pages 803-818, June.
    3. 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.
    4. Chien-Tai Lin & Shih-Chun Wang, 2015. "Discordancy tests for two-parameter exponential samples," Statistical Papers, Springer, vol. 56(2), pages 569-582, May.
    5. Nirpeksh Kumar, 2013. "A procedure for testing suspected observations," Statistical Papers, Springer, vol. 54(2), pages 471-478, May.
    6. Karol Pilot & Alicja Ganczarek-Gamrot & Krzysztof Kania, 2024. "Dealing with Anomalies in Day-Ahead Market Prediction Using Machine Learning Hybrid Model," Energies, MDPI, vol. 17(17), pages 1-20, September.
    7. Damian Przekop, 2020. "Feature Engineering for Anti-Fraud Models Based on Anomaly Detection," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 12(3), pages 301-316, September.
    8. Francesca Ieva & Anna Maria Paganoni, 2020. "Component-wise outlier detection methods for robustifying multivariate functional samples," Statistical Papers, Springer, vol. 61(2), pages 595-614, April.
    9. Gaucher, Solenne & Klopp, Olga & Robin, Geneviève, 2021. "Outlier detection in networks with missing links," Computational Statistics & Data Analysis, Elsevier, vol. 164(C).
    10. Andrzej Chmielowiec, 2021. "Algorithm for error-free determination of the variance of all contiguous subsequences and fixed-length contiguous subsequences for a sequence of industrial measurement data," Computational Statistics, Springer, vol. 36(4), pages 2813-2840, December.
    11. Marc Chataigner & Stéphane Crépey & Jiang Pu, 2020. "Nowcasting Networks," Post-Print hal-03910123, HAL.
    12. Greco, Salvatore & Ishizaka, Alessio & Tasiou, Menelaos & Torrisi, Gianpiero, 2019. "Sigma-Mu efficiency analysis: A methodology for evaluating units through composite indicators," European Journal of Operational Research, Elsevier, vol. 278(3), pages 942-960.
    13. Nicholas T. Longford, 2013. "Searching for contaminants," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(9), pages 2041-2055, September.
    14. David Juárez-Varón & Victoria Tur-Viñes & Alejandro Rabasa-Dolado & Kristina Polotskaya, 2020. "An Adaptive Machine Learning Methodology Applied to Neuromarketing Analysis: Prediction of Consumer Behaviour Regarding the Key Elements of the Packaging Design of an Educational Toy," Social Sciences, MDPI, vol. 9(9), pages 1-23, September.
    15. Stéphane Crépey & Lehdili Noureddine & Nisrine Madhar & Maud Thomas, 2022. "Anomaly Detection on Financial Time Series by Principal Component Analysis and Neural Networks," Working Papers hal-03777995, HAL.
    16. Zhongqiu Wang & Guan Yuan & Haoran Pei & Yanmei Zhang & Xiao Liu, 2020. "Unsupervised learning trajectory anomaly detection algorithm based on deep representation," International Journal of Distributed Sensor Networks, , vol. 16(12), pages 15501477209, December.
    17. Arata, Linda & Fabrizi, Enrico & Sckokai, Paolo, 2020. "A worldwide analysis of trend in crop yields and yield variability: Evidence from FAO data," Economic Modelling, Elsevier, vol. 90(C), pages 190-208.
    18. Wentao Yang & Huaxi He & Dongsheng Wei & Hao Chen, 2022. "Generating pseudo-absence samples of invasive species based on outlier detection in the geographical characteristic space," Journal of Geographical Systems, Springer, vol. 24(2), pages 261-279, April.
    19. Fournier, Nicholas PhD & Farid, Yashar Zeinali PhD & Patire, Anthony David PhD, 2021. "Potential Erroneous Degradation of High Occupancy Vehicle (HOV) Facilities," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt3z76r7tj, Institute of Transportation Studies, UC Berkeley.
    20. Richter, Lucas & Lehna, Malte & Marchand, Sophie & Scholz, Christoph & Dreher, Alexander & Klaiber, Stefan & Lenk, Steve, 2022. "Artificial Intelligence for Electricity Supply Chain automation," Renewable and Sustainable Energy Reviews, Elsevier, vol. 163(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:8:y:2020:i:12:p:2156-:d:455778. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.