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On adaptive linear regression

Author

Listed:
  • Arnab Maity
  • Michael Sherman

Abstract

Ordinary least squares (OLS) is omnipresent in regression modeling. Occasionally, least absolute deviations (LAD) or other methods are used as an alternative when there are outliers. Although some data adaptive estimators have been proposed, they are typically difficult to implement. In this paper, we propose an easy to compute adaptive estimator which is simply a linear combination of OLS and LAD. We demonstrate large sample normality of our estimator and show that its performance is close to best for both light-tailed (e.g. normal and uniform) and heavy-tailed (e.g. double exponential and t3) error distributions. We demonstrate this through three simulation studies and illustrate our method on state public expenditures and lutenizing hormone data sets. We conclude that our method is general and easy to use, which gives good efficiency across a wide range of error distributions.

Suggested Citation

  • Arnab Maity & Michael Sherman, 2008. "On adaptive linear regression," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(12), pages 1409-1422.
    • Handle: RePEc:taf:japsta:v:35:y:2008:i:12:p:1409-1422
    DOI: 10.1080/02664760802382475
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    References listed on IDEAS

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    1. Furno, Marilena, 1998. "Estimating the variance of the LAD regression coefficients," Computational Statistics & Data Analysis, Elsevier, vol. 27(1), pages 11-26, March.
    2. Newey, Whitney K., 1988. "Adaptive estimation of regression models via moment restrictions," Journal of Econometrics, Elsevier, vol. 38(3), pages 301-339, July.
    3. Phillips, P.C.B., 1991. "A Shortcut to LAD Estimator Asymptotics," Econometric Theory, Cambridge University Press, vol. 7(4), pages 450-463, December.
    4. McDonald, James B. & Newey, Whitney K., 1988. "Partially Adaptive Estimation of Regression Models via the Generalized T Distribution," Econometric Theory, Cambridge University Press, vol. 4(3), pages 428-457, December.
    5. Pollard, David, 1991. "Asymptotics for Least Absolute Deviation Regression Estimators," Econometric Theory, Cambridge University Press, vol. 7(2), pages 186-199, June.
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