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A Consistent Diagnostic Test For Regression Models Using Projections

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  • Escanciano, J. Carlos

Abstract

This paper proposes a consistent test for the goodness-of-fit of parametric regression models which overcomes two important problems of the existing tests, namely, the poor empirical power and size performance of the tests due to the curse of dimensionality and the choice of subjective parameters like bandwidths, kernels or integrating measures. We overcome these problems by using a residual marked empirical process based on projections (RMPP). We study the asymptotic null distribution of the test statistic and we show that our test is able to detect local alternatives converging to the null at the parametric rate. It turns out that the asymptotic null distribution of the test statistic depends on the data generating process, so a bootstrap procedure is considered. Our bootstrap test is robust to higher order dependence, in particular to conditional heteroskedasticity. For completeness, we propose a new minimum distance estimator constructed through the same RMPP as in the testing procedure. Therefore, the new estimator inherits all the good properties of the new test. We establish the consistency and asymptotic normality of the new minimum distance estimator. Finally, we present some Monte Carlo evidence that our testing procedure can play a valuable role in econometric regression modeling.

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Bibliographic Info

Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 22 (2006)
Issue (Month): 06 (December)
Pages: 1030-1051

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Handle: RePEc:cup:etheor:v:22:y:2006:i:06:p:1030-1051_06

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  1. Stinchcombe, Maxwell B. & White, Halbert, 1998. "Consistent Specification Testing With Nuisance Parameters Present Only Under The Alternative," Econometric Theory, Cambridge University Press, vol. 14(03), pages 295-325, June.
  2. Bierens, H.J. & Ploberger, W., 1995. "Asymptotic theory of integrated conditional moment tests," Discussion Paper, Tilburg University, Center for Economic Research 1995-124, Tilburg University, Center for Economic Research.
  3. Li, Qi & Hsiao, Cheng & Zinn, Joel, 2003. "Consistent specification tests for semiparametric/nonparametric models based on series estimation methods," Journal of Econometrics, Elsevier, Elsevier, vol. 112(2), pages 295-325, February.
  4. Juan Carlos Escanciano, 2005. "Goodness-of-fit Tests for Linear and Non-linear Time Series Models," Faculty Working Papers 02/05, School of Economics and Business Administration, University of Navarra.
  5. Gozalo, Pedro L., 1993. "A Consistent Model Specification Test for Nonparametric Estimation of Regression Function Models," Econometric Theory, Cambridge University Press, vol. 9(03), pages 451-477, June.
  6. Bierens, Herman J, 1990. "A Consistent Conditional Moment Test of Functional Form," Econometrica, Econometric Society, Econometric Society, vol. 58(6), pages 1443-58, November.
  7. Song Xi Chen & Wolfgang Härdle & Ming Li, 2003. "An empirical likelihood goodness-of-fit test for time series," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(3), pages 663-678.
  8. Li, Qi, 1999. "Consistent model specification tests for time series econometric models," Journal of Econometrics, Elsevier, Elsevier, vol. 92(1), pages 101-147, September.
  9. John Xu Zheng, 1996. "A consistent test of functional form via nonparametric estimation techniques," Journal of Econometrics, Elsevier, Elsevier, vol. 75(2), pages 263-289, December.
  10. Wooldridge, Jeffrey M., 1992. "A Test for Functional Form Against Nonparametric Alternatives," Econometric Theory, Cambridge University Press, vol. 8(04), pages 452-475, December.
  11. Bierens, Herman J., 1982. "Consistent model specification tests," Journal of Econometrics, Elsevier, Elsevier, vol. 20(1), pages 105-134, October.
  12. Whang, Yoon-Jae, 2000. "Consistent bootstrap tests of parametric regression functions," Journal of Econometrics, Elsevier, Elsevier, vol. 98(1), pages 27-46, September.
  13. Miles, Daniel & Mora, Juan, 2003. "On the performance of nonparametric specification tests in regression models," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 42(3), pages 477-490, March.
  14. Yatchew, Adonis John, 1992. "Nonparametric Regression Tests Based on Least Squares," Econometric Theory, Cambridge University Press, vol. 8(04), pages 435-451, December.
  15. Manuel A. Domínguez & Ignacio N. Lobato, 2004. "Consistent Estimation of Models Defined by Conditional Moment Restrictions," Econometrica, Econometric Society, Econometric Society, vol. 72(5), pages 1601-1615, 09.
  16. repec:cup:etheor:v:8:y:1992:i:4:p:435-51 is not listed on IDEAS
  17. Carrasco, Marine & Florens, Jean-Pierre, 2000. "Generalization Of Gmm To A Continuum Of Moment Conditions," Econometric Theory, Cambridge University Press, vol. 16(06), pages 797-834, December.
  18. Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, Econometric Society, vol. 57(6), pages 1403-30, November.
  19. Hong, Yongmiao & White, Halbert, 1995. "Consistent Specification Testing via Nonparametric Series Regression," Econometrica, Econometric Society, Econometric Society, vol. 63(5), pages 1133-59, September.
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  21. Winfried Stute, 2002. "Model Checks for Generalized Linear Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(3), pages 535-545.
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Citations

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Cited by:
  1. Lavergne, Pascal & Patilea, Valentin, 2008. "Breaking the curse of dimensionality in nonparametric testing," Journal of Econometrics, Elsevier, Elsevier, vol. 143(1), pages 103-122, March.
  2. Escanciano, Juan Carlos & Jacho-Chávez, David T., 2010. "Approximating the critical values of Cramér-von Mises tests in general parametric conditional specifications," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 54(3), pages 625-636, March.
  3. Pascal Lavergne & Valentin Patilea, 2008. "One for All and All for One:Regression Checks With Many Regressors," Discussion Papers dp08-06, Department of Economics, Simon Fraser University.
  4. Wasel Shadat, 2011. "On the Nonparametric Tests of Univariate GARCH Regression Models," The School of Economics Discussion Paper Series, Economics, The University of Manchester 1115, Economics, The University of Manchester.
  5. Carlos Escanciano, J., 2008. "Joint and marginal specification tests for conditional mean and variance models," Journal of Econometrics, Elsevier, Elsevier, vol. 143(1), pages 74-87, March.
  6. Juan Carlos Escanciano & Kyungchul Song, 2007. "Asymptotically Optimal Tests for Single-Index Restrictions with a Focus on Average Partial Effects," PIER Working Paper Archive 07-005, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  7. Miguel A. Delgado & Juan Carlos Escanciano, 2011. "Conditional stochastic dominance testing," Economics Working Papers we1138, Universidad Carlos III, Departamento de Economía.
  8. Escanciano, Juan Carlos & Song, Kyungchul, 2010. "Testing single-index restrictions with a focus on average derivatives," Journal of Econometrics, Elsevier, Elsevier, vol. 156(2), pages 377-391, June.
  9. Francesco Bravo, 2014. "Varying coefficients partially linear models with randomly censored data," Annals of the Institute of Statistical Mathematics, Springer, Springer, vol. 66(2), pages 383-412, April.
  10. Song, Kyungchul, 2010. "Testing semiparametric conditional moment restrictions using conditional martingale transforms," Journal of Econometrics, Elsevier, Elsevier, vol. 154(1), pages 74-84, January.
  11. Juan Carlos Escanciano, 2004. "Model Checks Using Residual Marked Empirical Processes," Faculty Working Papers 13/04, School of Economics and Business Administration, University of Navarra.
  12. Zhang, Jun & Feng, Zhenghui & Zhou, Bu, 2014. "A revisit to correlation analysis for distortion measurement error data," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 116-129.
  13. Andrea Vaona, 2008. "The sensitivity of nonparametric misspecification tests to disturbance autocorrelation," Quaderni della facoltà di Scienze economiche dell'Università di Lugano, USI Università della Svizzera italiana 0803, USI Università della Svizzera italiana.
  14. James Davidson & Andreea G. Halunga, 2013. "Consistent Model Specification Testing," Discussion Papers 1312, Exeter University, Department of Economics.

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