IDEAS home Printed from https://ideas.repec.org/a/taf/japsta/v35y2008i12p1409-1422.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://www.tandfonline.com/doi/abs/10.1080/02664760802382475
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/02664760802382475?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. 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.
    4. Phillips, P.C.B., 1991. "A Shortcut to LAD Estimator Asymptotics," Econometric Theory, Cambridge University Press, vol. 7(4), pages 450-463, December.
    5. Pollard, David, 1991. "Asymptotics for Least Absolute Deviation Regression Estimators," Econometric Theory, Cambridge University Press, vol. 7(2), pages 186-199, June.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Fong, Wai Mun, 1997. "Robust beta estimation: Some empirical evidence," Review of Financial Economics, Elsevier, vol. 6(2), pages 167-186.
    2. Masayuki Hirukawa & Mari Sakudo, 2016. "Testing Symmetry of Unknown Densities via Smoothing with the Generalized Gamma Kernels," Econometrics, MDPI, vol. 4(2), pages 1-27, June.
    3. Moreno, Marta, 1997. "Bootstrap tests for unit roots based on lad estimation," DES - Working Papers. Statistics and Econometrics. WS 6210, Universidad Carlos III de Madrid. Departamento de Estadística.
    4. Marcelo Fernandes & Eduardo Mendes & Olivier Scaillet, 2015. "Testing for symmetry and conditional symmetry using asymmetric kernels," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(4), pages 649-671, August.
    5. Haoying Wang, 2018. "Pricing used books on Amazon.com: a spatial approach to price dispersion," Spatial Economic Analysis, Taylor & Francis Journals, vol. 13(1), pages 99-117, January.
    6. Phillips, Peter C.B., 1995. "Robust Nonstationary Regression," Econometric Theory, Cambridge University Press, vol. 11(5), pages 912-951, October.
    7. Yiguo Sun & Thanasis Stengos, 2008. "The absolute health income hypothesis revisited: a semiparametric quantile regression approach," Empirical Economics, Springer, vol. 35(2), pages 395-412, September.
    8. Gupta, A, 2015. "Nonparametric specification testing via the trinity of tests," Economics Discussion Papers 15619, University of Essex, Department of Economics.
    9. Ximing Wu & Thanasis Stengos, 2005. "Partially adaptive estimation via the maximum entropy densities," Econometrics Journal, Royal Economic Society, vol. 8(3), pages 352-366, December.
    10. Arslan, Olcay, 2004. "Family of multivariate generalized t distributions," Journal of Multivariate Analysis, Elsevier, vol. 89(2), pages 329-337, May.
    11. Uwe Hassler & Paulo M.M. Rodrigues & Antonio Rubia, 2016. "Quantile Regression for Long Memory Testing: A Case of Realized Volatility," Journal of Financial Econometrics, Oxford University Press, vol. 14(4), pages 693-724.
    12. Chirok Han & Jin Seo Cho & Peter C. B. Phillips, 2011. "Infinite Density at the Median and the Typical Shape of Stock Return Distributions," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(2), pages 282-294, April.
    13. Tae-Hwan Kim & Halbert White, 2003. "Estimation, Inference, And Specification Testing For Possibly Misspecified Quantile Regression," Advances in Econometrics, in: Maximum Likelihood Estimation of Misspecified Models: Twenty Years Later, pages 107-132, Emerald Group Publishing Limited.
    14. Elise Coudin & Jean-Marie Dufour, 2017. "Finite-sample generalized confidence distributions and sign-based robust estimators in median regressions with heterogenous dependent errors," CIRANO Working Papers 2017s-06, CIRANO.
    15. McDonald, James B. & Xu, Yexiao J., 1995. "A generalization of the beta distribution with applications," Journal of Econometrics, Elsevier, vol. 69(2), pages 427-428, October.
    16. Chaohua Dong & Jiti Gao & Yundong Tu & Bin Peng, 2023. "Robust M-Estimation for Additive Single-Index Cointegrating Time Series Models," Papers 2301.06631, arXiv.org.
    17. Kenneth West & Ka-fu Wong & Stanislav Anatolyev, 2009. "Instrumental Variables Estimation of Heteroskedastic Linear Models Using All Lags of Instruments," Econometric Reviews, Taylor & Francis Journals, vol. 28(5), pages 441-467.
    18. Nannan Ma & Hailin Sang & Guangyu Yang, 2023. "Least absolute deviation estimation for AR(1) processes with roots close to unity," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(5), pages 799-832, October.
    19. Gupta, Abhimanyu, 2018. "Nonparametric specification testing via the trinity of tests," Journal of Econometrics, Elsevier, vol. 203(1), pages 169-185.
    20. Hansen, James V. & McDonald, James B. & Turley, Robert S., 2006. "Partially adaptive robust estimation of regression models and applications," European Journal of Operational Research, Elsevier, vol. 170(1), pages 132-143, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:taf:japsta:v:35:y:2008:i:12:p:1409-1422. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/CJAS20 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.