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Model selection for least absolute deviations regression in small samples

Author

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  • Hurvich, Clifford M.
  • Tsai, Chih-Ling

Abstract

We develop a small sample criterion (L1cAIC) for the selection of least absolute deviations regression models. In contrast to AIC (Akaike, 1973), L1cAIC provides an exactly unbiased estimator for the expected Kullback--Leibler information, assuming that the errors have a double exponential distribution and the model is not underfitted. In a Monte Carlo study, L1cAIC is found to perform much better than AIC and AICR (Ronchetti, 1985). A small sample criterion developed for normal least squares regression (cAIC, Hurvich and Tsai, 1988) is found to perform as well as L1cAIC. Further, cAIC is less computationally intensive than L1cAIC.

Suggested Citation

  • Hurvich, Clifford M. & Tsai, Chih-Ling, 1990. "Model selection for least absolute deviations regression in small samples," Statistics & Probability Letters, Elsevier, vol. 9(3), pages 259-265, March.
    • Handle: RePEc:eee:stapro:v:9:y:1990:i:3:p:259-265
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    Citations

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    Cited by:

    1. Jinfeng Xu & Zhiliang Ying, 2010. "Simultaneous estimation and variable selection in median regression using Lasso-type penalty," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 62(3), pages 487-514, June.
    2. Conde-Amboage, Mercedes & Sánchez-Sellero, César & González-Manteiga, Wenceslao, 2015. "A lack-of-fit test for quantile regression models with high-dimensional covariates," Computational Statistics & Data Analysis, Elsevier, vol. 88(C), pages 128-138.
    3. Arslan, Olcay, 2012. "Weighted LAD-LASSO method for robust parameter estimation and variable selection in regression," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1952-1965.
    4. Sandra L. Haire & Jonathan D. Coop & Carol Miller, 2017. "Characterizing Spatial Neighborhoods of Refugia Following Large Fires in Northern New Mexico USA," Land, MDPI, vol. 6(1), pages 1-24, March.
    5. Neath, Andrew A. & Cavanaugh, Joseph E., 2000. "A regression model selection criterion based on bootstrap bumping for use with resistant fitting," Computational Statistics & Data Analysis, Elsevier, vol. 35(2), pages 155-169, December.
    6. Lu, Xun & Su, Liangjun, 2015. "Jackknife model averaging for quantile regressions," Journal of Econometrics, Elsevier, vol. 188(1), pages 40-58.
    7. Lan Wang & Runze Li, 2009. "Weighted Wilcoxon-Type Smoothly Clipped Absolute Deviation Method," Biometrics, The International Biometric Society, vol. 65(2), pages 564-571, June.
    8. Halit DURAN, 2018. "Türki̇ye’De Devleti̇n Gi̇ri̇şi̇mci̇li̇k Destekleri̇ Ve Seçi̇lmi̇ş Bazi Deği̇şkenleri̇n Yeni̇ Fi̇rma Doğum Orani Üzeri̇ne Etki̇si̇," Journal of Research in Economics, Politics & Finance, Ersan ERSOY, vol. 3(1), pages 68-85.
    9. Çetin, Meral, 2009. "Robust model selection criteria for robust Liu estimator," European Journal of Operational Research, Elsevier, vol. 199(1), pages 21-24, November.

    More about this item

    Keywords

    AIC cAIC AICR L1 regression;

    JEL classification:

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

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