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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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  • Escanciano, J. Carlos, 2006. "A Consistent Diagnostic Test For Regression Models Using Projections," Econometric Theory, Cambridge University Press, vol. 22(06), pages 1030-1051, December.
  • Handle: RePEc:cup:etheor:v:22:y:2006:i:06:p:1030-1051_06
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    Citations

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    Cited by:

    1. 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.
    2. Carlos Escanciano, J., 2008. "Joint and marginal specification tests for conditional mean and variance models," Journal of Econometrics, Elsevier, vol. 143(1), pages 74-87, March.
    3. Brantly Callaway & Pedro H. C. Sant'Anna, 2018. "Difference-in-Differences with Multiple Time Periods and an Application on the Minimum Wage and Employment," Papers 1803.09015, arXiv.org.
    4. Andrea Vaona, 2008. "The sensitivity of nonparametric misspecification tests to disturbance autocorrelation," Quaderni della facoltà di Scienze economiche dell'Università di Lugano 0803, USI Università della Svizzera italiana.
    5. 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.
    6. Song, Kyungchul, 2010. "Testing semiparametric conditional moment restrictions using conditional martingale transforms," Journal of Econometrics, Elsevier, vol. 154(1), pages 74-84, January.
    7. Lavergne, Pascal & Patilea, Valentin, 2008. "Breaking the curse of dimensionality in nonparametric testing," Journal of Econometrics, Elsevier, vol. 143(1), pages 103-122, March.
    8. Wasel Shadat, 2011. "On the Nonparametric Tests of Univariate GARCH Regression Models," The School of Economics Discussion Paper Series 1115, Economics, The University of Manchester.
    9. Francesco Bravo, 2014. "Varying coefficients partially linear models with randomly censored data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(2), pages 383-412, April.
    10. Conde-Amboage, Mercedes & Sánchez-Sellero, César & González-Manteiga, Wenceslao, 2015. "A lack-of-fit test for quantile regression models with high-dimensional covariates," Computational Statistics & Data Analysis, Elsevier, vol. 88(C), pages 128-138.
    11. Pascal Lavergne & Valentin Patilea, 2011. "One for All and All for One: Regression Checks With Many Regressors," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(1), pages 41-52, January.
    12. Pedro H. C. Sant'Anna & Xiaojung Song, 2016. "Specification Tests for the Propensity Score," Papers 1611.06217, arXiv.org.
    13. repec:eee:jmvana:v:160:y:2017:i:c:p:10-30 is not listed on IDEAS
    14. 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.
    15. Sun, Zhihua & Chen, Feifei & Zhou, Xiaohua & Zhang, Qingzhao, 2017. "Improved model checking methods for parametric models with responses missing at random," Journal of Multivariate Analysis, Elsevier, vol. 154(C), pages 147-161.
    16. Escanciano, Juan Carlos & Song, Kyungchul, 2010. "Testing single-index restrictions with a focus on average derivatives," Journal of Econometrics, Elsevier, vol. 156(2), pages 377-391, June.
    17. Wang, Xuexin, 2015. "A Note on Consistent Conditional Moment Tests," MPRA Paper 69005, University Library of Munich, Germany.
    18. 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, vol. 54(3), pages 625-636, March.
    19. James Davidson & Andreea G. Halunga, 2013. "Consistent Model Specification Testing," Discussion Papers 1312, Exeter University, Department of Economics.
    20. Hongtu Zhu & Joseph G. Ibrahim & Ming-Hui Chen, 2015. "Diagnostic measures for the Cox regression model with missing covariates," Biometrika, Biometrika Trust, vol. 102(4), pages 907-923.
    21. Miguel A. Delgado & Juan Carlos Escanciano, 2013. "Conditional Stochastic Dominance Testing," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(1), pages 16-28, January.
    22. Hongtu Zhu & Joseph G. Ibrahim & Xiaoyan Shi, 2009. "Diagnostic Measures for Generalized Linear Models with Missing Covariates," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(4), pages 686-712.
    23. Jun Zhang & Nanguang Zhou & Zipeng Sun & Gaorong Li & Zhenghong Wei, 2016. "Statistical inference on restricted partial linear regression models with partial distortion measurement errors," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 70(4), pages 304-331, November.
    24. Chen, Tao & Tripathi, Gautam, 2017. "A simple consistent test of conditional symmetry in symmetrically trimmed tobit models," Journal of Econometrics, Elsevier, vol. 198(1), pages 29-40.
    25. Pedro H. C. Sant'Anna, 2016. "Program Evaluation with Right-Censored Data," Papers 1604.02642, arXiv.org.

    More about this item

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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