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Semiparametic Nonlinear Least-Squares Estimation of Truncated Regression Models

Published online by Cambridge University Press:  18 October 2010

Lung-Fei Lee
Affiliation:
University of Michigan

Abstract

This article provides a semiparametric method for the estimation of truncated regression models where the disturbances are independent of the regressors before truncation. This independence property provides useful information on model identification and estimation. Our estimate is shown to be -consistent and asymptotically normal. A consistent estimate of the asymptotic covariance matrix of the estimator is provided. Monte Carlo experiments are performed to investigate some finite sample properties of the estimator.

Type
Articles
Copyright
Copyright © Cambridge University Press 1992

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References

REFERENCES

1.Amemiya, T.Advanced Econometrics. Cambridge, MA: Harvard University Press, 1985.Google Scholar
2.Bhattacharya, P.K., Chernoff, H. & Yang, S.S.. Nonparametri c estimation of the slope of a truncated regression. The Annals of Statistics 11 (1983): 505514.CrossRefGoogle Scholar
3.Breiman, L., Tsur, Y. & Zemel, A.. Distribution-free estimators of censored regression models. Manuscript. Department of Economics, Ben Gurion University of the Negev, Israel, 1987.Google Scholar
4.Buckley, J. & James, I.. Linear regression with censored data. Biometrika 66 (1979): 429436.CrossRefGoogle Scholar
5.Cosslett, S.Efficiency bounds for distribution-free estimators of the censored regression models. Econometrica 55 (1987): 559585.CrossRefGoogle Scholar
6.Hoeffding, W.A class of statistics with asymptotically normal distribution. Annals of Mathematical Statistics 19 (1948): 293325.CrossRefGoogle Scholar
7.Horowitz, J.L.Semiparametric M estimation of censored linear regression models. Advances in Econometrics: Nonparametric and Robust Inference 1 (1988): 4583.Google Scholar
8.Ichimura, H. Estimation of single index models. Ph.D. Dissertation, MIT, Department of Economics, Boston, MA, 1987.Google Scholar
9.Ichimura, H. & Lee, L.F.. Semiparametric estimation of multiple index models: Single equation estimation. Forthcoming in Barnett, W.A., Powell, J., and Tauchen, G. (eds.) Nonpar-ametric and Semiparametric Methods in Econometrics and Statistics, Chapter 1. New York: Cambridge University Press, 1990.Google Scholar
10.James, I.R. & Smith, P.J.. Consistency results for linear regression with censored data. Annals of Statistics 12 (1984): 590600.CrossRefGoogle Scholar
11.Kaplan, E.L. & Meier, P.. Nonparametric estimation from incomplete observations. Journal of the American Statistical Association 53 (1958): 457481.CrossRefGoogle Scholar
12.Lee, M.J. Mode-Related Semiparametric Estimation of Censored and Truncated Models. Ph.D. Dissertation, University of Wisconsin, Department of Economics, Madison, WI, 1989.Google Scholar
13.Powell, J.L.Symmetrically trimmed least squares estimation for Tobit models. Econometrica 54 (1986): 14351460.CrossRefGoogle Scholar
14.Powell, J.L., Stock, J.H. & Stoker, T.M.. Semiparametric estimation of weighted average derivatives. Econometrica 57 (1989): 14031430.CrossRefGoogle Scholar
15.Rao, B.L.S.P.Nonparametric Functional Estimation. New York: Academic Press, 1983.Google Scholar
16.Ruud, P.A.Consistent estimation of limited dependent variable models despite misspeci-fication of distribution. Journal of Econometrics 32, Annals 1986–1 (1986): 157–187.CrossRefGoogle Scholar
17.Tsui, K.L., Jewell, N.P. & Wu, C.F.J.. A nonparametric approach to the truncated regression problem. Journal of the American Statistical Association 83 (1988): 785791.CrossRefGoogle Scholar
18.Vardi, Y.Empirical distribution in selection bias models. The Annals of Statistics 13 (1985): 178205.CrossRefGoogle Scholar