A Consistent Diagnostic Test For Regression Models Using Projections
AbstractThis paper proposes a consistent test for the goodness-of-fit of parametric regression models that 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 subjective choice of parameters such as bandwidths, kernels, and 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, and 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.The author thanks Carlos Velasco and Miguel A. Delgado for useful comments. The paper has also benefited from the comments of two referees and the co-editor. This research was funded by the Spanish Ministry of Education and Science reference number SEJ2004-04583 ECON and by the Universidad de Navarra reference number 16037001.
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Bibliographic InfoArticle provided by Cambridge University Press in its journal Econometric Theory.
Volume (Year): 22 (2006)
Issue (Month): 06 (December)
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Other versions of this item:
- Juan Carlos Escanciano, 2005. "A Consistent Diagnostic Test for Regression Models Using Projections," Faculty Working Papers 09/05, School of Economics and Business Administration, University of Navarra.
- 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
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- Wooldridge, Jeffrey M., 1992. "A Test for Functional Form Against Nonparametric Alternatives," Econometric Theory, Cambridge University Press, vol. 8(04), pages 452-475, December.
- Hong, Yongmiao & White, Halbert, 1995. "Consistent Specification Testing via Nonparametric Series Regression," Econometrica, Econometric Society, vol. 63(5), pages 1133-59, September.
- 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.
- Bierens, Herman J., 1982. "Consistent model specification tests," Journal of Econometrics, Elsevier, vol. 20(1), pages 105-134, October.
- 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.
- Chen, Song Xi & Härdle, Wolfgang & Kleinow, Torsten, 2000. "An empirical likelihood goodness-of-fit test for time series," SFB 373 Discussion Papers 2001,1, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
- Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, vol. 57(6), pages 1403-30, November.
- Miles, Daniel & Mora, Juan, 2003.
"On the performance of nonparametric specification tests in regression models,"
Computational Statistics & Data Analysis,
Elsevier, vol. 42(3), pages 477-490, March.
- Juan Mora & Daniel Miles, 2002. "On The Performance Of Nonparametric Specification Tests In Regression Models," Working Papers. Serie AD 2002-13, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
- Escanciano, J. Carlos, 2006.
"Goodness-of-Fit Tests for Linear and Nonlinear Time Series Models,"
Journal of the American Statistical Association,
American Statistical Association, vol. 101, pages 531-541, June.
- 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.
- 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.
- Bierens, H.J., 1989.
"A consistent conditional moment test of functional form,"
Serie Research Memoranda
0064, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
- Bierens, Herman J, 1990. "A Consistent Conditional Moment Test of Functional Form," Econometrica, Econometric Society, vol. 58(6), pages 1443-58, November.
- repec:cup:etheor:v:8:y:1992:i:4:p:435-51 is not listed on IDEAS
- Yatchew, Adonis John, 1992. "Nonparametric Regression Tests Based on Least Squares," Econometric Theory, Cambridge University Press, vol. 8(04), pages 435-451, December.
- 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.
- Li, Qi & Hsiao, Cheng & Zinn, Joel, 2003. "Consistent specification tests for semiparametric/nonparametric models based on series estimation methods," Journal of Econometrics, Elsevier, vol. 112(2), pages 295-325, February.
- Bierens, H.J. & Ploberger, W., 1995.
"Asymptotic theory of integrated conditional moment tests,"
1995-124, Tilburg University, Center for Economic Research.
- Herman J. Bierens & Werner Ploberger, 1997. "Asymptotic Theory of Integrated Conditional Moment Tests," Econometrica, Econometric Society, vol. 65(5), pages 1129-1152, September.
- Li, Qi, 1999. "Consistent model specification tests for time series econometric models," Journal of Econometrics, Elsevier, vol. 92(1), pages 101-147, September.
- repec:cup:etheor:v:8:y:1992:i:4:p:452-75 is not listed on IDEAS
- Whang, Yoon-Jae, 2000. "Consistent bootstrap tests of parametric regression functions," Journal of Econometrics, Elsevier, vol. 98(1), pages 27-46, September.
- Manuel A. Domínguez & Ignacio N. Lobato, 2004. "Consistent Estimation of Models Defined by Conditional Moment Restrictions," Econometrica, Econometric Society, vol. 72(5), pages 1601-1615, 09.
- 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.
- 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.
- Lavergne, Pascal & Patilea, Valentin, 2008.
"Breaking the curse of dimensionality in nonparametric testing,"
Journal of Econometrics,
Elsevier, vol. 143(1), pages 103-122, March.
- Pascal Lavergne & Valentin Patilea, 2006. "Breaking the Curse of Dimensionality in Nonparametric Testing," Working Papers 2006-24, Centre de Recherche en Economie et Statistique.
- Miguel A. Delgado & Juan Carlos Escanciano, 2011.
"Conditional stochastic dominance testing,"
Economics Working Papers
we1138, Universidad Carlos III, Departamento de Economía.
- James Davidson & Andreea G. Halunga, 2013. "Consistent Model Specification Testing," Discussion Papers 1312, Exeter University, Department of Economics.
- 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.
- Andrea Vaona, 2008. "The sensitivity of nonparametric misspecification tests to disturbance autocorrelation," Quaderni della facoltÃ di Scienze economiche dell'UniversitÃ di Lugano 0803, USI Università della Svizzera italiana.
- Pascal Lavergne & Valentin Patilea, 2008.
"One for All and All for One:Regression Checks With Many Regressors,"
dp08-06, Department of Economics, Simon Fraser University.
- Lavergne, Pascal & Patilea, Valentin, 2011. "One for all and all for one: regression checks with many regressors," MPRA Paper 35779, University Library of Munich, Germany.
- Pascal Lavergne & Valentin Patilea, 2007. "One for All and All for One : Regression Checks with Many Regressors”," Working Papers 2007-12, Centre de Recherche en Economie et Statistique.
- 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.
- 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.
- 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.
- 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.
- 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.
- Song, Kyungchul, 2010. "Testing semiparametric conditional moment restrictions using conditional martingale transforms," Journal of Econometrics, Elsevier, vol. 154(1), pages 74-84, January.
- Francesco Bravo, 2014. "Varying coefficients partially linear models with randomly censored data," Annals of the Institute of Statistical Mathematics, Springer, vol. 66(2), pages 383-412, April.
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