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Identification and classification of multiple outliers, high leverage points and influential observations in linear regression

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  • A.A.M. Nurunnabi
  • M. Nasser
  • A.H.M.R. Imon

Abstract

Detection of multiple unusual observations such as outliers, high leverage points and influential observations (IOs) in regression is still a challenging task for statisticians due to the well-known masking and swamping effects. In this paper we introduce a robust influence distance that can identify multiple IOs, and propose a sixfold plotting technique based on the well-known group deletion approach to classify regular observations, outliers, high leverage points and IOs simultaneously in linear regression. Experiments through several well-referred data sets and simulation studies demonstrate that the proposed algorithm performs successfully in the presence of multiple unusual observations and can avoid masking and/or swamping effects.

Suggested Citation

  • A.A.M. Nurunnabi & M. Nasser & A.H.M.R. Imon, 2016. "Identification and classification of multiple outliers, high leverage points and influential observations in linear regression," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(3), pages 509-525, March.
    • Handle: RePEc:taf:japsta:v:43:y:2016:i:3:p:509-525
    DOI: 10.1080/02664763.2015.1070806
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    References listed on IDEAS

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    1. Menjoge, Rajiv S. & Welsch, Roy E., 2010. "A diagnostic method for simultaneous feature selection and outlier identification in linear regression," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3181-3193, December.
    2. M. Habshah & M. R. Norazan & A.H.M. Rahmatullah Imon, 2009. "The performance of diagnostic-robust generalized potentials for the identification of multiple high leverage points in linear regression," Journal of Applied Statistics, Taylor & Francis Journals, vol. 36(5), pages 507-520.
    3. Billor, Nedret & Hadi, Ali S. & Velleman, Paul F., 2000. "BACON: blocked adaptive computationally efficient outlier nominators," Computational Statistics & Data Analysis, Elsevier, vol. 34(3), pages 279-298, September.
    4. Hadi, Ali S., 1992. "A new measure of overall potential influence in linear regression," Computational Statistics & Data Analysis, Elsevier, vol. 14(1), pages 1-27, June.
    5. A. H. M. Rahmatullah Imon, 2005. "Identifying multiple influential observations in linear regression," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(9), pages 929-946.
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