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Coefficients of determination for least absolute deviation analysis

Author

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  • McKean, Joseph W.
  • Sievers, Gerald L.

Abstract

The least-absolute deviation or l1 analysis of a linear model is an important alternative to the classical least squares analysis from the point of view of efficiency for longer-tailed error distributions and robustness to the presence of outliers. In this paper two coefficients of determination are proposed for the least-absolute deviation analysis. It is shown that they have desirable properties as measures of multiple association. Both fixed and random predictor variable cases are considered. In the case of random predictor variables, the sample coefficients of determination are shown to be consistent estimators of appropriate population parameters.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:5:y:1987:i:1:p:49-54
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    Cited by:

    1. Lei, Kaixuan & Chang, Jianxia & Wang, Yimin & Guo, Aijun & Huang, Mengdi & Xu, Bo, 2022. "Cascade hydropower stations short-term operation for load distribution considering water level synchronous variation," Renewable Energy, Elsevier, vol. 196(C), pages 683-693.
    2. Norling, Johannes, 2018. "Measuring heterogeneity in preferences over the sex of children," Journal of Development Economics, Elsevier, vol. 135(C), pages 199-221.
    3. Noh, Hohsuk & El Ghouch, Anouar & Van Keilegom, Ingrid, 2011. "On assessing model adequacy in linear quantile regression," LIDAM Discussion Papers ISBA 2011024, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    4. Ranganai, Edmore, 2016. "Quality of fit measurement in regression quantiles: An elemental set method approach," Statistics & Probability Letters, Elsevier, vol. 111(C), pages 18-25.
    5. Giulio Bottazzi & Marco Grazzi, 2014. "Dynamics Of Productivity And Cost Of Labour In Italian Manufacturing Firms," Bulletin of Economic Research, Wiley Blackwell, vol. 66(S1), pages 55-73, December.
    6. Sun, Rui-Bo & Wei, Bo-Cheng, 2004. "On influence assessment for LAD regression," Statistics & Probability Letters, Elsevier, vol. 67(2), pages 97-110, April.
    7. Noh, Hohsuk & El Ghouch, Anouar & Van Keilegom, Ingrid, 2013. "Assessing model adequacy in possibly misspecified quantile regression," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 558-569.
    8. Cristophe Croux & Catherine Dehon, 2003. "Estimators of the multiple correlation coefficient: Local robustness and confidence intervals," Statistical Papers, Springer, vol. 44(3), pages 315-334, July.
    9. Cheng, C.-L. & Shalabh, & Garg, G., 2016. "Goodness of fit in restricted measurement error models," Journal of Multivariate Analysis, Elsevier, vol. 145(C), pages 101-116.
    10. Cheng, C.-L. & Shalabh, & Garg, G., 2014. "Coefficient of determination for multiple measurement error models," Journal of Multivariate Analysis, Elsevier, vol. 126(C), pages 137-152.

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