İsmail YENİLMEZ, Yeliz MERT KANTAR, Şükrü ACITAŞ

ESTIMATION OF CENSORED REGRESSION MODEL IN THE CASE OF NON-NORMAL ERROR

For the censored regression model, it is well-known that while classical least squares estimation yields biased and nonconsistent estimator, maximum likelihood estimator (MLE) is consistent and efficient. Tobit estimator (Tobit model) based on MLE of normal error distribution is commonly-used estimation method for estimating censored regression in econometric literature. However, while the Tobit estimator works well for normal error distribution, its estimates may be inefficient in the case of non-normal errors. To solve this problem, different error distributions for the censored regression model have been proposed and tested in the literature. In this study, we consider the censored regression model based on the generalized logistic distribution. Generalized logistic distribution is very flexible distribution and approximates normal distribution for the special parameter cases. The considered estimator for the censored regression is evaluated by means of a simulation study designed in different combination of various error distributions and sample sizes. The results of the simulation show that the estimator of the censored regression model based on the generalized logistic distribution provides good performance for different error distributions and it is particularly good for small sample sizes. Moreover, when it is compared to classical Tobit estimator, efﬁciency loss of the considered estimator is very small for normal error distribution.

Keywords:

Censored dependent variable censored regression model, generalized logistic distribution, maximum likelihood estimation.,

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[1] Maddala, G.S. Limited-Dependent and Qualitative Variables in Econometrics. Cambridge, UK: Cambridge University Press, 1983.
[2] Tobin, J. Estimation of Relationships for Limited Dependent Variables. Econometrica, 26, 24-36, 1958.
[3] Pagan, A., Ullah, A. Nonparametric Ecometrics. Cambridge, UK: Cambridge University Press, 1999.
[4] Powell, J.L. Least Absolute Deviations Estimation of the Censored Regression Model. Econom 25:303-325, 1984.
[5] Powell, J.L. Symetrically trimmed least squares estimation for Tobit models. Econometrica 54:1435-1460, 1986.
[6] Caudill, S. B. A Partially Adaptive Estimator for The Censored Regression Model Based on A Mixture of Normal Distributions. Stats Methods Appl, 21:121-137, 2012.
[7] McDonald, J. B., Xu, Y. J. A Comparison of Semi-parametric and Partially Adaptive Estimators of the Censored Regression Model with Possibly Skewed and Leptokurtic Error Distributions. Economics Letter, 51(2), 153-159, 1996.
[8] Lewis, R. A., McDonald J. B. Partially Adaptive Estimation of the Censored Regression Model. Economic Reviews, 33 (7), 732-750, 2014.
[9] Arellano-Valle, R.B., Castro, L.M., González-Farías, G., Munoz-Gajardo, K.A. Student-t Censored Regression Model: Properties and Inference. Stat Methods Appl,21:453-473, 2012.
[10] Kantar, Y.M., Yenilmez, I., Acitas, S. Estimation based on generalized logistic distribution for the censored regression model. In Proceeding of the International Workshop on Mathematical Methods in Engineering. ISBN 978-975-6734-19-3, Cankaya University Press, 2017.
[11] Acitas, S., Yenilmez, I., Senoglu, B. and Kantar, Y. M. Modified Maximum Likelihood Estimation for the Censored Regression Model. The 13th IMT-GT International Conference on Mathematics, Statistics and Their Applications, Universiti Utara Malaysia December 4-7, 2017.
[12] Cohen, A.C. Truncated and Censored Samples: Theory and Applications. NY: Taylor & Francis Group, 1991.
[13] David, H. A. and Nagaraja, H. N.: Order Statistics, 3rd Edn.,Wiley, Hoboken, NJ, 458 pp., 2003.
[14] Wooldridge, J. Econometric Analysis of Cross Section and Panel Data, Cambridge: MIT Press, 2002.
[15] Fair, R. C. A Note on the Computation of the Tobit Estimator. Econometrica, 45(7):1723-7, 1977.
[16] Gupta, R. D., Kundu, D. Generalized logistic distributions. J. Appl. Statist., 18(1):51–66, 2010.
[17] Nassar, M.M., Elmasry, A. A study of generalized logistic distribution. Journal of the Egyption Mathematical Society, 20 126-133, 2012.
[18] Johnson, N.L., Kotz, S., Balakrishnan, N. Continuous Univariate Distributions, vol. 2, Wiley, New York, second ed., 1995.
[19] Balakrishnan, N., Leung, M. Y. Order statistics from the Type I generalized logistic distribution. Commun. Statist. Simulation Comput. 17(1):25–50, 1988.
[20] Zelterman, D. Parameter Estimation in the generalized logistic distribution. Comput. Stat. Data An. 5, 177–184, 1987.
[21] Shao, Q. Maximum likelihood estimation for Generalised logistic distributions. Communications in Statistics - Theory and Methods. 31:10, 1687-1700, 2002.
[22] Asgharzadeh, A. Point and interval estimation for a generalized logistic distribution under progressive type II censoring, Communications in Statistics - Theory and Methods, 35:9, 1685-1702, 2006.
[23] Kantar YM, Usta I, Acitas S. A Monte Carlo simulation study on partially adaptive estimators of linear regression models. J Appl Stat. 38(8), 1681–99, 2011.
[24] Yenilmez I., (2017) Limited Dependent Variable Models and Estimation Methods, MS Thesis, Graduate School of Sciences, Anadolu University, Eskisehir, Turkey.

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ISSN: 1304-7191
Yayın Aralığı: Yılda 4 Sayı
Yayıncı: Yıldız Teknik Üniversitesi

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