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Model checking in Tobit regression via nonparametric smoothing

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  • Koul, Hira L.
  • Song, Weixing
  • Liu, Shan

Abstract

This paper proposes a class of lack-of-fit tests for checking the adequacy of a presumed parametric form of the regression function in Tobit regression models. This class of tests is a weighted adaptation of the Zheng’s test for fitting a parametric regression model. The asymptotic null distributions of the underlying test statistics are shown to be normal. Moreover, the consistency of these tests against some fixed alternatives and asymptotic power against some local nonparametric alternatives are also derived. An optimal test within the proposed class of tests against a given sequence of nonparametric local alternatives is identified. A finite sample simulation shows some superiority of some of the proposed tests, compared to some of the existing tests.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:125:y:2014:i:c:p:36-49
    DOI: 10.1016/j.jmva.2013.11.017
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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. David M. Drukker, 2002. "Bootstrapping a conditional moments test for normality after tobit estimation," Stata Journal, StataCorp LP, vol. 2(2), pages 125-139, May.
    4. Arthur Lewbel & Oliver Linton, 2002. "Nonparametric Censored and Truncated Regression," Econometrica, Econometric Society, vol. 70(2), pages 765-779, March.
    5. 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.
    6. Amemiya, Takeshi, 1973. "Regression Analysis when the Dependent Variable is Truncated Normal," Econometrica, Econometric Society, vol. 41(6), pages 997-1016, November.
    7. 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.
    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. Lan Wang & Xiao-Hua Zhou, 2007. "Assessing the Adequacy of Variance Function in Heteroscedastic Regression Models," Biometrics, The International Biometric Society, vol. 63(4), pages 1218-1225, December.
    10. Zhang, Chunming & Dette, Holger, 2004. "A power comparison between nonparametric regression tests," Statistics & Probability Letters, Elsevier, vol. 66(3), pages 289-301, February.
    11. 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.
    12. 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.
    13. Powell, James L., 1984. "Least absolute deviations estimation for the censored regression model," Journal of Econometrics, Elsevier, vol. 25(3), pages 303-325, July.
    14. 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.
    15. Amemiya, Takeshi, 1984. "Tobit models: A survey," Journal of Econometrics, Elsevier, vol. 24(1-2), pages 3-61.
    16. Lopez, O. & Patilea, V., 2009. "Nonparametric lack-of-fit tests for parametric mean-regression models with censored data," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 210-230, January.
    17. 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.
    18. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
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