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The performance of diagnostic-robust generalized potentials for the identification of multiple high leverage points in linear regression

Author

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  • M. Habshah
  • M. R. Norazan
  • A.H.M. Rahmatullah Imon

Abstract

Leverage values are being used in regression diagnostics as measures of influential observations in the $X$-space. Detection of high leverage values is crucial because of their responsibility for misleading conclusion about the fitting of a regression model, causing multicollinearity problems, masking and/or swamping of outliers, etc. Much work has been done on the identification of single high leverage points and it is generally believed that the problem of detection of a single high leverage point has been largely resolved. But there is no general agreement among the statisticians about the detection of multiple high leverage points. When a group of high leverage points is present in a data set, mainly because of the masking and/or swamping effects the commonly used diagnostic methods fail to identify them correctly. On the other hand, the robust alternative methods can identify the high leverage points correctly but they have a tendency to identify too many low leverage points to be points of high leverages which is not also desired. An attempt has been made to make a compromise between these two approaches. We propose an adaptive method where the suspected high leverage points are identified by robust methods and then the low leverage points (if any) are put back into the estimation data set after diagnostic checking. The usefulness of our newly proposed method for the detection of multiple high leverage points is studied by some well-known data sets and Monte Carlo simulations.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:japsta:v:36:y:2009:i:5:p:507-520
    DOI: 10.1080/02664760802553463
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    References listed on IDEAS

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    1. Sung-Soo Kim & Sung Park & W. J. Krzanowski, 2008. "Simultaneous variable selection and outlier identification in linear regression using the mean-shift outlier model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(3), pages 283-291.
    2. Sung-Soo Kim & W. Krzanowski, 2007. "Detecting multiple outliers in linear regression using a cluster method combined with graphical visualization," Computational Statistics, Springer, vol. 22(1), pages 109-119, April.
    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. Sebert, David M. & Montgomery, Douglas C. & Rollier, Dwayne A., 1998. "A clustering algorithm for identifying multiple outliers in linear regression," Computational Statistics & Data Analysis, Elsevier, vol. 27(4), pages 461-484, June.
    6. 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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    1. 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.
    2. Hock Ann Lim & Habshah Midi, 2016. "Diagnostic Robust Generalized Potential Based on Index Set Equality (DRGP (ISE)) for the identification of high leverage points in linear model," Computational Statistics, Springer, vol. 31(3), pages 859-877, September.

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