Hostname: page-component-77c89778f8-m8s7h Total loading time: 0 Render date: 2024-07-16T16:37:22.246Z Has data issue: false hasContentIssue false

Winsorized Mean Estimator for Censored Regression

Published online by Cambridge University Press:  18 October 2010

Myoung-Jae Lee
Affiliation:
The Pennsylvania State University

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
Copyright
Copyright © Cambridge University Press 1992

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.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): 534.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): 5984.CrossRefGoogle Scholar
5. Horowitz, J.L. Semiparametric M-estimation of censored linear regression models. Advances in Econometrics 7 (1988): 4583.Google Scholar
6. Huber, P. Robust estimation of a location parameter. Annals of Mathematical Statistics 35 (1964): 73101.CrossRefGoogle Scholar
7. Huber, P. The behavior of maximum likelihood estimates under nonstandard conditions. Proceedings of the 5th Berkeley Symposium 1 (1967): 221233.Google Scholar
8. Huber, P. Robust regression: Asymptotics, conjectures and Monte-Carlo. Annals of Statistics 1 (1973): 799821.CrossRefGoogle Scholar
9. Knight, K. Limit theory for M-estimates in an integrated infinite variance process. Econometric Theory 1 (1991): 200212.CrossRefGoogle Scholar
10. Lee, M.J. Mode regression. Journal of Econometrics 42 (1989): 337349.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): 99135.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): 295317.CrossRefGoogle Scholar
15. Pakes, A. & Pollard, D.. Simulation and the asymptotics of optimization estimator. Econometrica 57 (1989): 10271057.CrossRefGoogle Scholar
16. Phillips, P.C.B. A shortcut to LAD estimator asymptotics. Econometric Theory 7 (1991): 450463.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): 186199.CrossRefGoogle Scholar
19. Powell, J.L. Least absolute deviations estimation for the censored regression model. Journal of Econometrics 25 (1984): 303325.CrossRefGoogle Scholar
20. Powell, J.L. Symmetriclaly trimmed least squares estimation for Tobit models. Econometrica 54 (1986): 14351460.CrossRefGoogle Scholar
21. Powell, J.L., Stock, J.H. & Stoker, T.S.. Semiparametric estimation of index coefficients. Econometrica 57 (1989): 14031430.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): 828838.CrossRefGoogle Scholar