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Empirical L2-distance lack-of-fit tests for Tobit regression models

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  • Song, Weixing
  • Zhang, Yi

Abstract

Standard Tobit regression models assume a linear relationship between the partially observed response variable and the predictors, while applications often see some nonlinear connections. This paper proposes an empirical L2-distance lack-of-fit test to check the adequacy of the presumed parametric form for the regression function in Tobit regression models. The proposed test statistic is shown to be asymptotically normal, consistent against some fixed alternatives, and has nontrivial power for some local nonparametric alternatives. Simulation studies are conducted to assess the finite sample performance of the proposed test.

Suggested Citation

  • Song, Weixing & Zhang, Yi, 2012. "Empirical L2-distance lack-of-fit tests for Tobit regression models," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 380-396.
    • Handle: RePEc:eee:jmvana:v:111:y:2012:i:c:p:380-396
    DOI: 10.1016/j.jmva.2012.04.015
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    References listed on IDEAS

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    1. Wang, Lan, 2007. "A simple nonparametric test for diagnosing nonlinearity in Tobit median regression model," Statistics & Probability Letters, Elsevier, vol. 77(10), pages 1034-1042, June.
    2. James J. Heckman, 1976. "The Common Structure of Statistical Models of Truncation, Sample Selection and Limited Dependent Variables and a Simple Estimator for Such Models," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 5, number 4, pages 475-492, National Bureau of Economic Research, Inc.
    3. Heckman, James, 2013. "Sample selection bias as a specification error," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 31(3), pages 129-137.
    4. Amemiya, Takeshi, 1973. "Regression Analysis when the Dependent Variable is Truncated Normal," Econometrica, Econometric Society, vol. 41(6), pages 997-1016, November.
    5. Akinwumi A. Adesina & Moses M. Zinnah, 1993. "Technology characteristics, farmers' perceptions and adoption decisions: A Tobit model application in Sierra Leone," Agricultural Economics, International Association of Agricultural Economists, vol. 9(4), pages 297-311, December.
    6. Lin, Tsai-Fen & Schmidt, Peter, 1984. "A Test of the Tobit Specification against an Alternative Suggested by Cragg," The Review of Economics and Statistics, MIT Press, vol. 66(1), pages 174-177, February.
    7. Nelson, Forrest D, 1981. "A Test for Misspecification in the Censored Normal Model," Econometrica, Econometric Society, vol. 49(5), pages 1317-1329, September.
    8. Horowitz, Joel L & Neumann, George R, 1989. "Specification Testing in Censored Regression Models: Parametric and Semiparametric Methods," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 4(S), pages 61-86, Supplemen.
    9. John Xu Zheng, 1996. "A consistent test of functional form via nonparametric estimation techniques," Journal of Econometrics, Elsevier, vol. 75(2), pages 263-289, December.
    10. Adesina, Akinwumi A. & Zinnah, Moses M., 1993. "Technology characteristics, farmers' perceptions and adoption decisions: A Tobit model application in Sierra Leone," Agricultural Economics, Blackwell, vol. 9(4), pages 297-311, December.
    11. Olsen, Randall J, 1980. "Approximating a Truncated Normal Regression with the Method of Moments," Econometrica, Econometric Society, vol. 48(5), pages 1099-1105, July.
    12. Powell, James L., 1984. "Least absolute deviations estimation for the censored regression model," Journal of Econometrics, Elsevier, vol. 25(3), pages 303-325, July.
    13. Amemiya, Takeshi, 1984. "Tobit models: A survey," Journal of Econometrics, Elsevier, vol. 24(1-2), pages 3-61.
    14. Hall, Peter, 1984. "Central limit theorem for integrated square error of multivariate nonparametric density estimators," Journal of Multivariate Analysis, Elsevier, vol. 14(1), pages 1-16, February.
    15. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
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    Cited by:

    1. Koul, Hira L. & Song, Weixing & Liu, Shan, 2014. "Model checking in Tobit regression via nonparametric smoothing," Journal of Multivariate Analysis, Elsevier, vol. 125(C), pages 36-49.

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