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Student-t censored regression model: properties and inference

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  • Reinaldo Arellano-Valle

    ()

  • Luis Castro

    ()

  • Graciela González-Farías

    ()

  • Karla Muñoz-Gajardo

    ()

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    Abstract

    In statistical analysis, particularly in econometrics, it is usual to consider regression models where the dependent variable is censored (limited). In particular, a censoring scheme to the left of zero is considered here. In this article, an extension of the classical normal censored model is developed by considering independent disturbances with identical Student-t distribution. In the context of maximum likelihood estimation, an expression for the expected information matrix is provided, and an efficient EM-type algorithm for the estimation of the model parameters is developed. In order to know what type of variables affect the income of housewives, the results and methods are applied to a real data set. A brief review on the normal censored regression model or Tobit model is also presented. Copyright Springer-Verlag 2012

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    Bibliographic Info

    Article provided by Springer in its journal Statistical Methods & Applications.

    Volume (Year): 21 (2012)
    Issue (Month): 4 (November)
    Pages: 453-473

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    Handle: RePEc:spr:stmapp:v:21:y:2012:i:4:p:453-473

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    Related research

    Keywords: ECM algorithm; Limited dependent variable; Maximum likelihood estimation; Student-t distribution; Tobit model;

    References

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    1. Arellano-Valle, R. B. & del Pino, G. & San Martín, E., 2002. "Definition and probabilistic properties of skew-distributions," Statistics & Probability Letters, Elsevier, vol. 58(2), pages 111-121, June.
    2. Amemiya, Takeshi, 1973. "Regression Analysis when the Dependent Variable is Truncated Normal," Econometrica, Econometric Society, Econometric Society, vol. 41(6), pages 997-1016, November.
    3. Blundell, Richard & Meghir, Costas, 1987. "Bivariate alternatives to the Tobit model," Journal of Econometrics, Elsevier, Elsevier, vol. 34(1-2), pages 179-200.
    4. Michelli Barros & Manuel Galea & Manuel González & Víctor Leiva, 2010. "Influence diagnostics in the tobit censored response model," Statistical Methods and Applications, Springer, Springer, vol. 19(3), pages 379-397, August.
    5. Amemiya, Takeshi, 1984. "Tobit models: A survey," Journal of Econometrics, Elsevier, Elsevier, vol. 24(1-2), pages 3-61.
    6. Thomas Mroz, . "The Sensitivity of an Empirical Model of Married Women's Hours of Work to Economic and Statistical Assumptions," University of Chicago - Population Research Center, Chicago - Population Research Center 84-8, Chicago - Population Research Center.
    7. Arellano-Valle, Reinaldo B. & Genton, Marc G., 2008. "On the exact distribution of the maximum of absolutely continuous dependent random variables," Statistics & Probability Letters, Elsevier, vol. 78(1), pages 27-35, January.
    8. Olsen, Randall J, 1978. "Note on the Uniqueness of the Maximum Likelihood Estimator for the Tobit Model," Econometrica, Econometric Society, Econometric Society, vol. 46(5), pages 1211-15, September.
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