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An equality test across nonparametric regressions

  • Lavergne, Pascal

A procedure for testing equality across nonparametric regressions is proposed. The procedure allows for any dimension of the explanatory variables and for any number of subsamples. We consider the case of random explanatory variables and allow the designs of the regressors and the number of observations to dier across subsamples. The division into subsamples is defined through a variable C which can be either fixed or random. In the case of a random C, our procedure is a general test of significance for qualitative variables in a nonparametric regression. In the case of a fixed C, our procedure provides a 'nonparametric analysis of covariance'. In both case, the test is a one-sided normal test and is consistent against all alternatives. We study its small sample behavior through Monte-Carlo simulations.

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Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 103 (2001)
Issue (Month): 1-2 (July)
Pages: 307-344

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Handle: RePEc:eee:econom:v:103:y:2001:i:1-2:p:307-344
Contact details of provider: Web page: http://www.elsevier.com/locate/jeconom

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  1. Lavergne, Pascal & Vuong, Quang, 1998. "Nonparametric significance testing," SFB 373 Discussion Papers 1998,75, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  2. Aït-Sahalia, Yacine. & Bickel, Peter J. & Stoker, Thomas M., 1994. "Goodness-of-fit tests for regression using kernel methods," Working papers 3747-94., Massachusetts Institute of Technology (MIT), Sloan School of Management.
  3. 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.
  4. Li, Qi, 1999. "Consistent model specification tests for time series econometric models," Journal of Econometrics, Elsevier, vol. 92(1), pages 101-147, September.
  5. Chamberlain, Gary, 1984. "Panel data," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 22, pages 1247-1318 Elsevier.
  6. 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.
  7. Hall, Peter, 1984. "Central limit theorem for integrated square error of multivariate nonparametric density estimators," Journal of Multivariate Analysis, Elsevier, vol. 14(1), pages 1-16, February.
  8. Delgado, Miguel A., 1993. "Testing the equality of nonparametric regression curves," Statistics & Probability Letters, Elsevier, vol. 17(3), pages 199-204, June.
  9. King, Eileen & Hart, Jeffrey D. & Wehrly, Thomas E., 1991. "Testing the equality of two regression curves using linear smoothers," Statistics & Probability Letters, Elsevier, vol. 12(3), pages 239-247, September.
  10. Baltagi, Badi H. & Hidalgo, Javier & Li, Qi, 1996. "A nonparametric test for poolability using panel data," Journal of Econometrics, Elsevier, vol. 75(2), pages 345-367, December.
  11. Lavergne, P. & Vuong, Q., 1992. "Nonparametric Selection of Regressors : the Nonnested Case," Papers 9204, Southern California - Department of Economics.
  12. Fan, Yanqin & Li, Qi, 1996. "Consistent Model Specification Tests: Omitted Variables and Semiparametric Functional Forms," Econometrica, Econometric Society, vol. 64(4), pages 865-90, July.
  13. E. Guerre & Pascal Lavergne, 2000. "Minimax Rates for Nonparametric Specification Testing in Regression Models," Econometric Society World Congress 2000 Contributed Papers 0644, Econometric Society.
  14. Yatchew, A., 1999. "An elementary nonparametric differencing test of equality of regression functions," Economics Letters, Elsevier, vol. 62(3), pages 271-278, March.
  15. Delgado, Miguel A & Mora, Juan, 1995. "Nonparametric and Semiparametric Estimation with Discrete Regressors," Econometrica, Econometric Society, vol. 63(6), pages 1477-84, November.
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