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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.

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Bibliographic Info

Article provided by Elsevier in its journal Statistics & Probability Letters.

Volume (Year): 17 (1993)
Issue (Month): 3 (June)
Pages: 199-204

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Handle: RePEc:eee:stapro:v:17:y:1993:i:3:p:199-204

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Related research

Keywords: Nonparametric testing weighted empirical process Donsker's invariance principle Brownian motion local alternatives;

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Cited by:
  1. Scheike, Thomas H., 2000. "Comparison of non-parametric regression functions through their cumulatives," Statistics & Probability Letters, Elsevier, vol. 46(1), pages 21-32, January.
  2. 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.
  3. Lavergne, Pascal, 2001. "An equality test across nonparametric regressions," Journal of Econometrics, Elsevier, vol. 103(1-2), pages 307-344, July.
  4. Aitor Ciarreta & María Paz Espinosa, 2003. "Market Power In The Spanish Wholesale Electricity Market," Working Papers. Serie AD 2003-22, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  5. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
  6. E. Guerre & Pascal Lavergne, 2000. "Minimax Rates for Nonparametric Specification Testing in Regression Models," Econometric Society World Congress 2000 Contributed Papers 0644, Econometric Society.
  7. Yatchew, A., 1999. "An elementary nonparametric differencing test of equality of regression functions," Economics Letters, Elsevier, vol. 62(3), pages 271-278, March.
  8. Srihera, Ramidha & Stute, Winfried, 2010. "Nonparametric comparison of regression functions," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 2039-2059, October.
  9. 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, vol. 50(2), pages 253-275, June.
  10. Gørgens, Tue, 2002. "Nonparametric comparison of regression curves by local linear fitting," Statistics & Probability Letters, Elsevier, vol. 60(1), pages 81-89, November.
  11. 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.
  12. Park, Joon Y. & Whang, Yoon-Jae, 2004. "A Test of the Martingale Hypothesis," Working Papers 2004-11, Rice University, Department of Economics.
  13. Ignacio N. Lobato, 2000. "A Consistent Test for the Martingale Difference Assumption," Econometric Society World Congress 2000 Contributed Papers 0278, Econometric Society.
  14. Dette, Holger & Neumeyer, Natalie, 2000. "Nonparametric analysis of covariance," Technical Reports 2000,42, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
  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. 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.

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