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Testing the equality of nonparametric regression curves

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  • Delgado, Miguel A.

Abstract

This paper proposes a test for the equality of nonparametric regression curves that does not depend on the choice of a smoothing number. The test statistic resembles in spirit the Kolmogorov-Smirnov statistic and it is easy to compute. It is powerful under alternatives that converge to the null hypothesis at a rate n-1/2. The disturbance distributions are arbitrary and possibly unequal, and conditions on the regressors distribution are very mild. A Monte Carlo study illustrates the performance of the test in small and moderate samples. We also study extensions to multiple regression, and test the equality of several regression curves.

Suggested Citation

  • Delgado, Miguel A., 1993. "Testing the equality of nonparametric regression curves," Statistics & Probability Letters, Elsevier, vol. 17(3), pages 199-204, June.
  • Handle: RePEc:eee:stapro:v:17:y:1993:i:3:p:199-204
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    Citations

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    Cited by:

    1. Hira Koul & Fang Li, 2005. "Testing for Superiority among Two Time Series," Statistical Inference for Stochastic Processes, Springer, vol. 8(2), pages 109-135, September.
    2. Lavergne, Pascal, 2001. "An equality test across nonparametric regressions," Journal of Econometrics, Elsevier, vol. 103(1-2), pages 307-344, July.
    3. Delgado, Miguel A. & Domínguez, Manuel A., 1997. "Consistent specification testing of quantile regression models," DES - Working Papers. Statistics and Econometrics. WS 6211, Universidad Carlos III de Madrid. Departamento de Estadística.
    4. Gørgens, Tue, 2002. "Nonparametric comparison of regression curves by local linear fitting," Statistics & Probability Letters, Elsevier, vol. 60(1), pages 81-89, November.
    5. Srihera, Ramidha & Stute, Winfried, 2010. "Nonparametric comparison of regression functions," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 2039-2059, October.
    6. Masamune Iwasawa, 2015. "A Joint Specification Test for Response Probabilities in Unordered Multinomial Choice Models," Econometrics, MDPI, Open Access Journal, vol. 3(3), pages 1-31, September.
    7. Ignacio N. Lobato, 2000. "A Consistent Test for the Martingale Difference Assumption," Econometric Society World Congress 2000 Contributed Papers 0278, Econometric Society.
    8. Aitor Ciarreta & María Espinosa, 2010. "Market power in the Spanish electricity auction," Journal of Regulatory Economics, Springer, vol. 37(1), pages 42-69, February.
    9. Park Joon Y. & Whang Yoon-Jae, 2005. "A Test of the Martingale Hypothesis," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 9(2), pages 1-32, June.
    10. Park, Cheolwoo & Kang, Kee-Hoon, 2008. "SiZer analysis for the comparison of regression curves," Computational Statistics & Data Analysis, Elsevier, vol. 52(8), pages 3954-3970, April.
    11. Aitor Ciarreta & María Paz Espinosa, 2006. "Demand Elasticity and Market Power in the Spanish Electricity Market," Working Papers 0606, Departament Empresa, Universitat Autònoma de Barcelona, revised Jun 2006.
    12. Dette, Holger & Neumeyer, Natalie, 2000. "Nonparametric analysis of covariance," Technical Reports 2000,42, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    13. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, number 8355.
    14. Scheike, Thomas H., 2000. "Comparison of non-parametric regression functions through their cumulatives," Statistics & Probability Letters, Elsevier, vol. 46(1), pages 21-32, January.
    15. 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.
    16. Scholz, Achim & Neumeyer, Natalie & Munk, Axel, 2004. "Nonparametric Analysis of Covariance : the Case of Inhomogeneous and Heteroscedastic Noise," Technical Reports 2004,28, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    17. Yatchew, A., 1999. "An elementary nonparametric differencing test of equality of regression functions," Economics Letters, Elsevier, vol. 62(3), pages 271-278, March.
    18. Juan Carlos Pardo-Fernández & María Dolores Jiménez-Gamero & Anouar El Ghouch, 2015. "A Non-parametric ANOVA-type Test for Regression Curves Based on Characteristic Functions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(1), pages 197-213, March.
    19. E. Guerre & Pascal Lavergne, 2000. "Minimax Rates for Nonparametric Specification Testing in Regression Models," Econometric Society World Congress 2000 Contributed Papers 0644, Econometric Society.
    20. Holger Dette & Axel Munk, 1998. "A Simple Goodness-of-fit Test for Linear Models Under a Random Design Assumption," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(2), pages 253-275, June.
    21. Masamune Iwasawa, 2015. "Joint Specification Tests For Response Probabilities In Unordered Multinomial Choice Models," KIER Working Papers 919, Kyoto University, Institute of Economic Research.
    22. Dette, Holger & Neumeyer, Natalie, 2000. "Nonparametric comparison of regression curves - an empirical process approach," Technical Reports 2000,62, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.

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