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LAD Regression for Detecting Outliers in Response and Explanatory Variables

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  • Dodge, Yadolah

Abstract

Least absolute deviations regression resists outliers in the response variable but is relatively sensitive to outlying observations in the explanatory variables. In this paper a simple solution is proposed to overcome this problem. This is achieved by minimizing the absolute values of vertical and horizontal deviations in turn. Two algorithms are proposed: one for the simple and one for the multiple regression case. The methods presented have been tested on a variety of data and have proven to be quite effective.

Suggested Citation

  • Dodge, Yadolah, 1997. "LAD Regression for Detecting Outliers in Response and Explanatory Variables," Journal of Multivariate Analysis, Elsevier, vol. 61(1), pages 144-158, April.
    • Handle: RePEc:eee:jmvana:v:61:y:1997:i:1:p:144-158
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    References listed on IDEAS

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    1. Dielman, Terry E. & Rose, Elizabeth L., 1996. "A note on hypothesis testing in LAV multiple regression: A small sample comparison," Computational Statistics & Data Analysis, Elsevier, vol. 21(4), pages 463-470, April.
    2. Dielman, Terry E. & Rose, Elizabeth L., 1995. "A bootstrap approach to hypothesis testing in least absolute value regression," Computational Statistics & Data Analysis, Elsevier, vol. 20(2), pages 119-130, August.
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    Cited by:

    1. Sun, Rui-Bo & Wei, Bo-Cheng, 2004. "On influence assessment for LAD regression," Statistics & Probability Letters, Elsevier, vol. 67(2), pages 97-110, April.
    2. Barbato, Michele & Ceselli, Alberto, 2024. "Mathematical programming for simultaneous feature selection and outlier detection under l1 norm," European Journal of Operational Research, Elsevier, vol. 316(3), pages 1070-1084.
    3. Nathan Sudermann-Merx & Steffen Rebennack, 2021. "Leveraged least trimmed absolute deviations," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 43(3), pages 809-834, September.
    4. Rosaria Romano & Francesco Palumbo, 2021. "Partial possibilistic regression path modeling: handling uncertainty in path modeling," Computational Statistics, Springer, vol. 36(1), pages 615-639, March.
    5. Yadolah Dodge & Ali Hadi, 1999. "Simple graphs and bounds for the elements of the hat matrix," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(7), pages 817-823.
    6. Kadriye Hilal Topal & Ebru Çağlayan Akay, 2020. "Hanehalkı Tüketim Harcamalarının Mikroekonometrik Analizi: LAD-LASSO Yöntemi," EKOIST Journal of Econometrics and Statistics, Istanbul University, Faculty of Economics, vol. 0(33), pages 13-31, December.

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