Abstract
The goal of this paper is to introduce a partially adaptive estimator for the censored regression model based on an error structure described by a mixture of two normal distributions. The model we introduce is easily estimated by maximum likelihood using an EM algorithm adapted from the work of Bartolucci and Scaccia (Comput Stat Data Anal 48:821–834, 2005). A Monte Carlo study is conducted to compare the small sample properties of this estimator to the performance of some common alternative estimators of censored regression models including the usual tobit model, the CLAD estimator of Powell (J Econom 25:303–325, 1984), and the STLS estimator of Powell (Econometrica 54:1435–1460, 1986). In terms of RMSE, our partially adaptive estimator performed well. The partially adaptive estimator is applied to data on wife’s hours worked from Mroz (1987). In this application we find support for the partially adaptive estimator over the usual tobit model.
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References
Amemiya T (1985) Advanced econometrics. Harvard University Press, Cambridge
Bartolucci F, Scaccia L (2005) The use of mixtures for dealing with non-normal regression errors. Comput Stat Data Anal 48: 821–834
Beran R (1974) Asymptotically efficient adaptive rank estimates in location models. Ann Stat 2: 63–74
Bickel PJ (1982) On adaptive estimation. Ann Stat 10: 647–671
Buchinsky M (1994) Changes in the U.S. wage structure 1963–1987: application of quantile regression. Econometrica 62: 405–458
Butler RJ, McDonald JB, Nelson RD, White SB (1990) Robust and partially adaptive estimation of regression models. Rev Econ Stat 2: 321–327
Cizek P (2008) Semiparametric robust estimation of truncated and censored regression models. Tilburg University, Department of Econometrics & Operations Research, CentER Discussion Paper Series No. 2008-34
Dempster AP, Laird NM, Rubin DB (1977) Maximum likelihood estimation from incomplete data via the EM algorithm. J R Stat Soc Ser B 39: 1–38
Geweke J, Keane M (1997) Mixture-of-normals Probit. Federal Reserve Bank of Minneapolis, Research Staff Report 237, Aug 1997
Hansen CB, McDonald JB, Theodossiou P (2007) Some flexible parametric models for partially adaptive estimators of econometric models. Economics, The Open-Access Open Assessment E-journal. No. 2007-70e
Honore BE (1992) Trimmed LAD and least squares estimation of truncated and censored regression models with fixed effects. Econometrica 60: 533–565
Honore BE, Hu L (2007) Estimation of cross sectional and panel data censored regression models with endogeneity. J Econom 122: 293–316
Honore BE, Powell JE (1994) Pairwise difference estimators for censored and truncated regression models. J Econom 64: 241–278
Hu L (2002) Estimation of a censored dynamic panel data. Econometrica 70: 2499–2517
Khan S, Powell JL (2001) Two-step estimation of semiparametric censored regression models. J Econom 103: 73–110
Kwak S, Lee J, Russell C (1997) Dealing with censored data from contingent valuation surveys: Symmetrically-trimmed least squares estimation. South Econ J 63:743–750
Lee MJ (1993) Quadratic mode regression. J Econom 57: 1–19
Manski CF (1984) Adaptive estimation of non-linear regression models. Econom Rev 3: 145–194
McDonald JB (1996) An application and comparison of some flexible parametric and semi-parametric qualitative response models. Econ Lett 53: 145–152
McDonald JB, Newey WK (1988) Partially adaptive estimation of regression models via the generalized T distribution. Econom Theory 4: 428–457
McDonald JB, White SB (1993) A comparison of some robust, adaptive, and partially adaptive estimators of regression models. Econom Rev 12: 103–124
McDonald JB, Xu YJ (1996) A comparison of semi-parametric and partially adaptive estimators of the censored regression model with possibly skewed and leptokurtic error distributions. Econ Lett 51: 153–159
Moon C (1989) A Monte Carlo comparison of semiparametric Tobit estimators. J Appl Econom 4: 361–382
Mroz T (1987) The sensitivity of an empiricial model of married women’s hours of work to economic and statistical assumptions. Econometrica 55:765–799
Paarsch H (1984) A Monte Carlo comparison of estimators for censored regression models. J Econom 24: 197–213
Pagan A, Ullah A (1999) Nonparametric econometrics. Cambridge University Press, Cambridge
Phillips RF (1991) A constrained maximum likelihood approach to estimating switching regressions. J Econom 48: 241–262
Phillips RF (1994) Partially adaptive estimation via a normal mixture. J Econom 64: 123–144
Portnoy S (2003) Censored regression quantiles. J Am Stat Assoc 98: 1001–1012
Powell JL (1984) Least absolute deviations estimation of the censored regression model. J Econom 25: 303–325
Powell JL (1986) Symmetrically trimmed least squares estimation for Tobit models. Econometrica 54: 1435–1460
Quandt R (1988) The econometrics of disequilibrium. Blackwell, Oxford
Sarstedt M, Schwaiger M (2008) Model selection in mixture regression analysis-a Monte Carlo simulation study. In: Data analysis, machine learning and applications: Proceedings of the 31st annual conference of the Gesellschaft fur Klassifikation. ed.V., Albert-Ludwigs-Univesitat Freiburg, 7–9 March. Springer, Berlin, pp 61–68
Stein C (1956) Efficient nonparametric testing and estimation. Proc 3rd Berkeley Symp Math Stat Probab 1: 187–195
Stone C (1984) Adaptive maximum likelihood estimators of a location parameter. Ann Stat 3: 267–284
Wu X, Stengos T (2005) Partially Adaptive Estimation via the Maximum Entropy Densities. Econom J 9: 1–15
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Caudill, S.B. A partially adaptive estimator for the censored regression model based on a mixture of normal distributions. Stat Methods Appl 21, 121–137 (2012). https://doi.org/10.1007/s10260-011-0182-z
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DOI: https://doi.org/10.1007/s10260-011-0182-z