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Procedures for the identification of multiple influential observations in linear regression

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  • A.A.M. Nurunnabi
  • Ali S. Hadi
  • A.H.M.R. Imon

Abstract

Since the seminal paper by Cook (1977) in which he introduced Cook's distance, the identification of influential observations has received a great deal of interest and extensive investigation in linear regression. It is well documented that most of the popular diagnostic measures that are based on single-case deletion can mislead the analysis in the presence of multiple influential observations because of the well-known masking and/or swamping phenomena. Atkinson (1981) proposed a modification of Cook's distance. In this paper we propose a further modification of the Cook's distance for the identification of a single influential observation. We then propose new measures for the identification of multiple influential observations, which are not affected by the masking and swamping problems. The efficiency of the new statistics is presented through several well-known data sets and a simulation study.

Suggested Citation

  • A.A.M. Nurunnabi & Ali S. Hadi & A.H.M.R. Imon, 2014. "Procedures for the identification of multiple influential observations in linear regression," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(6), pages 1315-1331, June.
    • Handle: RePEc:taf:japsta:v:41:y:2014:i:6:p:1315-1331
    DOI: 10.1080/02664763.2013.868418
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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. 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.
    3. 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.
    4. A. A. M. Nurunnabi & A.H.M. Rahmatullah Imon & M. Nasser, 2010. "Identification of multiple influential observations in logistic regression," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(10), pages 1605-1624.
    5. Nguyen, T.D. & Welsch, R., 2010. "Outlier detection and least trimmed squares approximation using semi-definite programming," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3212-3226, December.
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    Cited by:

    1. Junlong Zhao & Chao Liu & Lu Niu & Chenlei Leng, 2019. "Multiple influential point detection in high dimensional regression spaces," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 81(2), pages 385-408, April.

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