Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-24T18:36:12.337Z Has data issue: false hasContentIssue false
  • English
  • Français

A Comparison of Ordinary Least Squares and Least Absolute Error Estimation

Published online by Cambridge University Press:  18 October 2010

Andrew A. Weiss
Andrew A. Weiss*
Affiliation:
University of Southern California
Get access Rights & Permissions [Opens in a new window]

Abstract

In a linear-regression model with heteroscedastic errors, we consider two tests: a Hausman test comparing the ordinary least squares (OLS) and least absolute error (LAE) estimators and a test based on the signs of the errors from OLS. It turns out that these are related by the well-known equivalence between Hausman and the generalized method of moments tests. Particular cases, including homoscedasticity and asymmetry in the errors, are discussed.

Type
Brief Report
Information
Econometric Theory , Volume 4 , Issue 3 , December 1988 , pp. 517 - 527
Copyright
Copyright © Cambridge University Press 1988 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1. Antille, A., Kersting, G. & Zucchini, W.. Testing asymmetry. Journal of the American Statistical Association 77 (1982): 639–646.Google Scholar
2. Boos, D.D. A test for asymmetry associated with the Hodges–Lehmann estimator. Journal of the American Statistical Association 77 (1982): 647–651.10.1080/01621459.1982.10477864Google Scholar
3. Brown, B.M. & Kildea, D.G.. Outlier-detection tests and robust estimators based on signs of residuals. Communications in Statistics A8 (1979): 257–269.10.1080/03610927908827757Google Scholar
4. Domowitz, I. New directions in nonlinear estimation with dependent observations. Canadian Journal of Economics 18 (1985): 1–27.Google Scholar
5. Hausman, J.A. Specification tests in econometrics. Econometrica 46 (1978): 1251–1272.10.2307/1913827Google Scholar
6. Huber, P.J. The behavior of maximum-likelihood estimates under nonstandard conditions. In Le Cam, L.M. & Neyman, J. (eds.), Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, Volume 1, pp 221–233. California: University of California Press, 1967.Google Scholar
7. Johnston, J. Econometric methods. Third Edition. New York: McGraw Hill, 1984.Google Scholar
8. Koenker, R. & Bassett, G.. Tests of linear hypotheses and l 1 estimation. Econometrica 50 (1982): 1577–1583.Google Scholar
9. Newey, W.K. Generalized method of moments specification testing. Journal of Econometrics 29 (1985): 229–256.10.1016/0304-4076(85)90154-XGoogle Scholar
10. Newey, W.K. & Powell, J.L.. Asymmetric least-squares estimation. Econometrica 55 (1987): 819–847.Google Scholar
11. Powell, J.L. Least absolute deviations estimation for the censored regression model. Journal of Econometrics 25 (1984): 303–325.Google Scholar
12. Ruppert, D. & Carroll, R.J.. Trimmed least-squares estimation in the linear model. Journal of the American Statistical Association 75 (1980): 828–838.10.1080/01621459.1980.10477560Google Scholar
13. Ruud, P.A. Tests of specification in econometrics. Econometric Review 3 (1984): 211–242.10.1080/07474938408800065Google Scholar
14. Weiss, A.A. Estimating nonlinear dynamic models using least absolute error estimation. MRG Working Paper #M8630, revised, Department of Economics, University of Southern California, 1987.Google Scholar
15. White, H. Asymptotic theory for econometricians. New York: Academic Press, 1984.Google Scholar
16. White, H. & Domowitz, I.. Nonlinear regression with dependent observations. Econometrica 52 (1984): 143–161.Google Scholar