Least absolute deviations estimation for the censored regression model

doi:10.1016/0304-4076(84)90004-6

Journal of Econometrics

Volume 25, Issue 3, July 1984, Pages 303-325

https://doi.org/10.1016/0304-4076(84)90004-6 Get rights and content

Abstract

This paper proposes an alternative to maximum likelihood estimation of the parameters of the censored regression (or censored ‘Tobit’) model. The proposed estimator is a generalization of least absolute deviations estimation for the standard linear model, and, unlike estimation methods based on the assumption of normally distributed error terms, the estimator is consistent and asymptotically normal for a wide class of error distributions, and is also robust to heteroscedasticity. The paper gives the regularity conditions and proofs of these large-sample results, and proposes classes of consistent estimators of the asymptotic covariance matrix for both homoscedastic and heteroscedastic disturbances.

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^☆: This research was supported by National Science Foundation Grants SES79-12965 and SES79-13976 at the Institute for Mathematical Studies in the Social Sciences at Stanford University. I would like to thank Takeshi Amemiya, Theodore W. Anderson, Timothy Bresnahan, Colin Cameron, Jerry Hausman, Thomas MaCurdy, Daniel McFadden, Julio Rotemberg, and the referees for their helpful comments.

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Least absolute deviations estimation for the censored regression model☆

Abstract

Journal of Econometrics

Regression analysis when the dependent variable is truncated normal

Econometrica

Two stage least absolute deviations estimators

Econometrica

An investigation of the robustness of the Tobit estimator to non-normality

Econometrica

Asymptotic theory of least absolute error regression

Journal of the American Statistical Association

One-step Huber estimation in the linear model

Journal of the American Statistical Association

Linear regression with censored data

Biometrika

Maximum likelihood from incomplete data via the EM algorithm

Journal of the Royal Statistical Society B

Abnormal selection bias

Specification tests in econometrics

Econometrica

The common structure of statistical models of truncation, sample selection, and limited dependent variables and a simple estimator for such models

Annals of Economic and Social Measurement

Sample bias as a specification error

Econometrica

Robust estimation of a location parameter

Annals of Mathematical Statistics

The behavior of maximum likelihood estimates under nonstandard conditions

Proceedings of the Fifth Berkeley Symposium

Asymptotic relations of M-estimates and R-estimates in the linear model

Annals of Statistics