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On influence assessment for LAD regression

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  • Sun, Rui-Bo
  • Wei, Bo-Cheng

Abstract

Least absolute deviations (LAD) regression, i.e. L1 regression, is more resistant to the outliers in the response variable than the least-squares regression, but is relatively sensitive to outlying observations in explanatory variables. However, some but few attentions have been contributed to the influence assessment for LAD regression, especially for LAD nonlinear regression. In this paper, we propose several diagnostic measures, which can be used for LAD regression models. The quasi-likelihood distance based on the L1 objective function, Cook distance based on the elliptical norm and some other diagnostic measures are introduced for LAD regression, and two examples are given to illustrate the use of these measures. The diagnostic models for LAD regression are also investigated. It is proved that the estimators of the case deletion model (CDM) and the mean shift outlier model (MSOM) are equal in linear and nonlinear LAD regression models.

Suggested Citation

  • Sun, Rui-Bo & Wei, Bo-Cheng, 2004. "On influence assessment for LAD regression," Statistics & Probability Letters, Elsevier, vol. 67(2), pages 97-110, April.
    • Handle: RePEc:eee:stapro:v:67:y:2004:i:2:p:97-110
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    References listed on IDEAS

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    1. Wang, J. D., 1995. "Asymptotic Normality of L1-Estimators in Nonlinear Regression," Journal of Multivariate Analysis, Elsevier, vol. 54(2), pages 227-238, August.
    2. McKean, Joseph W. & Sievers, Gerald L., 1987. "Coefficients of determination for least absolute deviation analysis," Statistics & Probability Letters, Elsevier, vol. 5(1), pages 49-54, January.
    3. Bo‐Cheng Wei & Yue‐Qing Hu & Wing‐Kam Fung, 1998. "Generalized Leverage and its Applications," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 25(1), pages 25-37, March.
    4. Tang, Nian-Sheng & Wei, Bo-Cheng & Wang, Xue-Ren, 2000. "Influence diagnostics in nonlinear reproductive dispersion models," Statistics & Probability Letters, Elsevier, vol. 46(1), pages 59-68, January.
    5. Bo-Cheng Wei & Jian-Qing Shih, 1994. "On statistical models for regression diagnostics," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(2), pages 267-278, June.
    6. 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.
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    Cited by:

    1. Vanegas, Luis Hernando & Rondón, Luz Marina & Cysneiros, Francisco José A., 2012. "Diagnostic procedures in Birnbaum–Saunders nonlinear regression models," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1662-1680.
    2. Vanegas, Luis Hernando & Cysneiros, Francisco José A., 2010. "Assessment of diagnostic procedures in symmetrical nonlinear regression models," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 1002-1016, April.

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    More about this item

    Keywords

    Diagnostics Inferential measure LAD regression L1 objective function Nonlinear regression Quasi-likelihood distance;

    JEL classification:

    • L1 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance

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