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Winsorized Mean Estimator for Censored Regression

Published online by Cambridge University Press:  18 October 2010

Myoung-Jae Lee
Myoung-Jae Lee
Affiliation:
The Pennsylvania State University
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Abstract

We introduce a semiparametric estimator for the censored linear regression model. It is based on the regression version of Huber's [6] M-estimator. It includes Powell's [19] censored least absolute deviations estimator as a special case and is related to Powell's [20] symmetrically censored least-squares estimator. We prove strong consistency and derive its asymptotic distribution which is √n-consistent with an easily computable covariance matrix. A small-scale simulation study shows that it works quite well in various cases.

Type
Articles
Information
Econometric Theory , Volume 8 , Issue 3 , September 1992 , pp. 368 - 382
Copyright
Copyright © Cambridge University Press 1992

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References

REFERENCES

1.Amemiya, T. Advanced Econometrics. Cambridge: Harvard University Press, 1985.Google Scholar
2. Duncan, G.M. A semi-parametric censored regression estimator. Journal of Econometrics 32 (1986): 5–34.CrossRefGoogle Scholar
3. Hampel, F.R., Ronchetti, EL., Rousseeuw, P.J. & Stahel, W.A.. Robust Statistics. New York: Wiley, 1986.Google Scholar
4. Horowitz, J.L.A distribution free LSE for censored linear regression models. Journal of Econometrics 32 (1986): 59–84.CrossRefGoogle Scholar
5. Horowitz, J.L. Semiparametric M-estimation of censored linear regression models. Advances in Econometrics 7 (1988): 45–83.Google Scholar
6. Huber, P. Robust estimation of a location parameter. Annals of Mathematical Statistics 35 (1964): 73–101.CrossRefGoogle Scholar
7. Huber, P. The behavior of maximum likelihood estimates under nonstandard conditions. Proceedings of the 5th Berkeley Symposium 1 (1967): 221–233.Google Scholar
8. Huber, P. Robust regression: Asymptotics, conjectures and Monte-Carlo. Annals of Statistics 1 (1973): 799–821.CrossRefGoogle Scholar
9. Knight, K. Limit theory for M-estimates in an integrated infinite variance process. Econometric Theory 1 (1991): 200–212.CrossRefGoogle Scholar
10. Lee, M.J. Mode regression. Journal of Econometrics 42 (1989): 337–349.CrossRefGoogle Scholar
11. Lee, M.J. Median regression for ordered discrete response. Journal of Econometrics (1992): forthcoming.CrossRefGoogle Scholar
12. Lee, M.J. Quadratic mode regression. Journal of Econometrics (1992): forthcoming.Google Scholar
13. Newey, W.K. Semiparametric efficiency bounds. Journal of Applied Econometrics 5 (1990): 99–135.CrossRefGoogle Scholar
14. Newey, W.K. & Powell, J.L.. Efficient estimation of linear and type I censored regression models under conditional quantile restrictions. Econometric Theory 6 (1990): 295–317.CrossRefGoogle Scholar
15. Pakes, A. & Pollard, D.. Simulation and the asymptotics of optimization estimator. Econometrica 57 (1989): 1027–1057.CrossRefGoogle Scholar
16. Phillips, P.C.B. A shortcut to LAD estimator asymptotics. Econometric Theory 7 (1991): 450–463.CrossRefGoogle Scholar
17. Pollard, D. Convergence of Stochastic Processes. New York: Springer-Verlag, 1984.CrossRefGoogle Scholar
18. Pollard, D. Asymptotics for least absolute deviation regression estimators. Econometric Theory 1 (1991): 186–199.CrossRefGoogle Scholar
19. Powell, J.L. Least absolute deviations estimation for the censored regression model. Journal of Econometrics 25 (1984): 303–325.CrossRefGoogle Scholar
20. Powell, J.L. Symmetriclaly trimmed least squares estimation for Tobit models. Econometrica 54 (1986): 1435–1460.CrossRefGoogle Scholar
21. Powell, J.L., Stock, J.H. & Stoker, T.S.. Semiparametric estimation of index coefficients. Econometrica 57 (1989): 1403–1430.CrossRefGoogle Scholar
22. Press, W.H., Flannery, B.P. & Teukolsky, S.A.. Numerical Recipes: The Art of Computing. New York: Cambridge University Press, 1986.Google Scholar
23. Ruppert, D. & Caroll, R.J.. Trimmed least squares estimation in the linear model. The Journal of the American Statistical Association 75 (1980): 828–838.CrossRefGoogle Scholar