A partially adaptive estimator for the censored regression model based on a mixture of normal distributions

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.

[1]  Robert F. Phillips.  A constrained maximum-likelihood approach to estimating switching regressions☆ , 1991 .

[2]  Bronwyn H Hall,et al.  Estimation and Inference in Nonlinear Structural Models , 1974 .

[3]  Rudolf Beran,et al.  Asymptotically Efficient Adaptive Rank Estimates in Location Models , 1974 .

[4]  Darryl Holden,et al.  Testing the Normality Assumption in the Tobit Model , 2004 .

[5]  Steven B. Caudill,et al.  Estimating a mixture of stochastic frontier regression models via the em algorithm: A multiproduct cost function application , 2003 .

[6]  Brenton R. Clarke,et al.  Comment on "Estimating mixtures of normal distributions and switching regressions" by Quandt and Ramsey , 1978 .

[7]  N. Mendell,et al.  Simulated percentage points for the null distribution of the likelihood ratio test for a mixture of two normals. , 1988, Biometrics.

[8]  P. Bickel.  On Adaptive Estimation , 1982 .

[9]  Richard E. Quandt,et al.  The Econometrics Of Disequilibrium , 1988 .

[10]  A. Ullah,et al.  Nonparametric Econometrics , 1999 .

[11]  Harry J. Paarsch.  A Monte Carlo comparison of estimators for censored regression models , 1984 .

[12]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[13]  James B. McDonald,et al.  A comparison of some robust, adaptive, and partially adaptive estimators of regression models , 1993 .

[14]  C. Stein.  Efficient Nonparametric Testing and Estimation , 1956 .

[15]  Bo E. Honoré,et al.  Pairwise difference estimators of censored and truncated regression models , 1994 .

[16]  Panayiotis Theodossiou,et al.  Some Flexible Parametric Models for Partially Adaptive Estimators of Econometric Models , 2007 .

[17]  Steven B. Caudill,et al.  More on testing the normality assumptionin the Tobit Model , 2009 .

[18]  J. Geweke,et al.  Mixture of normals probit models , 1997 .

[19]  Robert F. Phillips.  Partially adaptive estimation via a normal mixture , 1994 .

[20]  K. D. Kumar,et al.  Comment on “Estimating Mixtures of Normal Distributions and Switching Regressions” , 1979 .

[21]  Francesco Bartolucci,et al.  The use of mixtures for dealing with non-normal regression errors , 2004, Comput. Stat. Data Anal..

[22]  Stephen Portnoy,et al.  Censored Regression Quantiles , 2003 .

[23]  Luojia Hu,et al.  Estimation of a Censored Dynamic Panel Data Model , 2002 .

[24]  Moshe Buchinsky.  CHANGES IN THE U.S. WAGE STRUCTURE 1963-1987: APPLICATION OF QUANTILE REGRESSION , 1994 .

[25]  Douglas G. Steigerwald.  On the finite sample behavior of adaptive estimators , 1992 .

[26]  Ping Zhang,et al.  The effects of the gender of children on expenditure patterns in rural China: a semiparametric analysis , 2005 .

[27]  Richard J. Butler,et al.  Robust and Partially Adaptive Estimation of Regression Models , 1990 .

[28]  James B. McDonald,et al.  A Comparison of Partially Adaptive and Reweighted Least Squares Estimation , 2003 .

[29]  James B. McDonald,et al.  An application and comparison of some flexible parametric and semi-parametric qualitative response models , 1996 .

[30]  Robert A. Moffitt,et al.  The Uses of Tobit Analysis , 1980 .

[31]  Qi Li,et al.  Adaptive Estimation in the Panel Data Error Component Model with Heteroskedasticity of Unknown Form , 1994 .

[32]  Charles F. Manski,et al.  Adaptive estimation of non–linear regression models , 1984 .

[33]  M. Wand,et al.  EXACT MEAN INTEGRATED SQUARED ERROR , 1992 .

[34]  James B. McDonald,et al.  Partially Adaptive Estimation of Regression Models via the Generalized T Distribution , 1988, Econometric Theory.

[35]  W. N. Street,et al.  Financial Data and the Skewed Generalized T Distribution , 1998 .

[36]  James L. Powell,et al.  Symmetrically Trimmed Least Squares Estimation For Tobit Models , 1986 .

[37]  Steven B. Caudill,et al.  Do former athletes make better managers? Evidence from a partially adaptive grouped-data regression model , 2010 .

[38]  P. Čížek,et al.  Semiparametric Robust Estimation of Truncated and Censored Regression Models , 2008 .

[39]  J. Powell,et al.  Least absolute deviations estimation for the censored regression model , 1984 .

[40]  Thanasis Stengos,et al.  Partially Adaptive Estimation Via the Maximum Entropy Densities , 2005 .

[41]  T. Mroz,et al.  The Sensitivity of an Empirical Model of Married Women's Hours of Work to Economic and Statistical Assumptions , 1987 .

[42]  Bo E. Honoré,et al.  Estimation of cross sectional and panel data censored regression models with endogeneity , 2004 .

[43]  H. Bozdogan.  Model selection and Akaike's Information Criterion (AIC): The general theory and its analytical extensions , 1987 .

[44]  A. Ullah,et al.  Nonparametric Econometrics: Semiparametric and Nonparametric Estimation of Simultaneous Equation Models , 1999 .

[45]  Tue Gørgens,et al.  Semiparametric Estimation of Single-Index Hazard Functions Without Proportional Hazards , 2006 .

[46]  James L. Powell,et al.  Two-step estimation of semiparametric censored regression models , 2001 .

[47]  Carol Alexander,et al.  Option Pricing with Normal Mixture Returns: Modelling Excess Kurtosis and Uncertanity in Volatility , 2001 .

[48]  James B. McDonald,et al.  A comparison of semi-parametric and partially adaptive estimators of the censored regression model with possibly skewed and leptokurtic error distributions , 1996 .

[49]  Bo E. Honoré,et al.  Trimmed LAD and Least Squares Estimation of Truncated and Censored Regression Models with Fixed Effects , 1992 .

[50]  Marko Sarstedt,et al.  Model Selection in Mixture Regression Analysis-A Monte Carlo Simulation Study , 2007, GfKl.

[51]  Myoung-jae Lee,et al.  QUADRATIC MODE REGRESSION , 1993 .

[52]  Marko Sarstedt,et al.  Sample- and segment-size specific Model Selection in Mixture Regression Analysis , 2006 .

[53]  C. J. Stone,et al.  Adaptive Maximum Likelihood Estimators of a Location Parameter , 1975 .

[54]  Clifford S. Russell,et al.  Dealing with censored data from contingent valuation surveys: Symmetrically-trimmed least squares estimation , 1997 .

[55]  Choon-Geol Moon,et al.  A Monte Carlo Comparison of Semiparametric Tobit Estimators , 1989 .

[56]  Alain Monfort,et al.  Pricing and Inference with Mixtures of Conditionally Normal Processes , 2007 .