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Testing parametric conditional distributions using the nonparametric smoothing method

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Abstract

This paper proposes a new goodness-of-fit test for parametric conditional probability distributions using the nonparametric smoothing methodology. An asymptotic normal distribution is established for the test statistic under the null hypothesis of correct specification of the parametric distribution. The test is shown to have power against local alternatives converging to the null at certain rates. The test can be applied to testing for possible misspecifications in a wide variety of parametric models. A bootstrap procedure is provided for obtaining more accurate critical values for the test. Monte Carlo simulations show that the test has good power against some common alternatives.

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References

  • Aït-Sahalia Y, Bickel PJ, Stoker TM (2001) Goodness-of-fit tests for regression using Kernel methods. J Economet 105: 363–412

    Article  MATH  Google Scholar 

  • Andrews DWK (1997) A conditional Kolmogorov test. Econometrica 65: 1097–1128

    Article  MathSciNet  MATH  Google Scholar 

  • Bai J (2003) Testing parametric conditional distributions of hynamic models. Rev Econ Stat 85: 531–549

    Article  Google Scholar 

  • Bickel PJ, Rosenblatt M (1973) On some global measures of the deviations of density function Estimates. Ann Stat 1: 1071–1095 [Correction: 3 (1975) 1370]

    Article  MathSciNet  MATH  Google Scholar 

  • Bickel PJ, Ritov Y, Stoker TM (2006) Tailor-made tests for goodness of fit to semiparametric hypotheses. Ann Stat 34: 721–741

    Article  MathSciNet  MATH  Google Scholar 

  • Eubank RL, Hart JD, LaRiccia VN (1993) Testing goodness of fit via nonparametric function estimation techniques. Commun Stat 22: 3327–3354

    Article  MathSciNet  MATH  Google Scholar 

  • Eubank RL, LaRiccia VN (1992) Asymptotic comparison of cramér-von mises and nonparametric function estimation techniques for testing goodness-of-fit. Ann Stat 20: 2071–2086

    Article  MathSciNet  MATH  Google Scholar 

  • Eubank RL, LaRiccia VN, Rosenstein R (1987) Test statistics derived as components of Pearson’s Phi-squared distance measure. J Am Stat Assoc 82: 816–825

    MathSciNet  MATH  Google Scholar 

  • Ghosh BK, Huang W (1991) The power and optimal Kernel of the Bickel-Rosenblatt test for the goodness-of-fit. Ann Stat 19: 999–1009

    Article  MathSciNet  MATH  Google Scholar 

  • Hall P (1984) Central limit Theorem for integrated square error of multivariate nonparametric density estimators. J Multivar Anal 14: 1–16

    Article  MATH  Google Scholar 

  • Hart JD (1997) Nonparametric smoothing and lack-of-fit tests. Springer, New York

    MATH  Google Scholar 

  • Powell JL, Stock JH, Stoker TM (1989) Semiparametric estimation of index coefficients. Econometrica 57: 1403–1430

    Article  MathSciNet  MATH  Google Scholar 

  • Rosenblatt M (1975) A quadratic measure of deviation of two-dimensional density estimates and a test of independence. Ann Stat 3: 1–14 [Correction: 10 (1982) 646]

    Article  MathSciNet  MATH  Google Scholar 

  • Zheng JX (2000) A consistent test of conditional parametric distributions. Economet Theory 16: 667–691

    Article  MATH  Google Scholar 

  • Zheng X (2008) Testing for discrete choice models. Econ Lett 98: 176–184

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. School of Economics, Antai College of Economics and Management, Shanghai Jiao Tong University, 200052, Shanghai, China

    Xu Zheng

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  1. Xu Zheng
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Correspondence to Xu Zheng.

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I thank the two anonymous referees for helpful comments.

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Zheng, X. Testing parametric conditional distributions using the nonparametric smoothing method. Metrika 75, 455–469 (2012). https://doi.org/10.1007/s00184-010-0336-2

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  • DOI: https://doi.org/10.1007/s00184-010-0336-2

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