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An equality test across nonparametric regressions

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  • Lavergne, Pascal

Abstract

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.

Suggested Citation

  • Lavergne, Pascal, 1998. "An equality test across nonparametric regressions," SFB 373 Discussion Papers 1998,79, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    • Handle: RePEc:zbw:sfb373:199879
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    Cited by:

    1. Sianesi, Barbara, 2017. "Evidence of randomisation bias in a large-scale social experiment: The case of ERA," Journal of Econometrics, Elsevier, vol. 198(1), pages 41-64.
    2. Christopher F. Parmeter & Jeffrey S. Racine, 2018. "Nonparametric Estimation and Inference for Panel Data Models," Department of Economics Working Papers 2018-02, McMaster University.
    3. Lavergne, Pascal & Maistre, Samuel & Patilea, Valentin, 2014. "A Significance Test for Covariates in Nonparametric Regression," TSE Working Papers 14-502, Toulouse School of Economics (TSE).
    4. Lavergne, Pascal & Patilea, Valentin, 2008. "Breaking the curse of dimensionality in nonparametric testing," Journal of Econometrics, Elsevier, vol. 143(1), pages 103-122, March.
    5. Srihera, Ramidha & Stute, Winfried, 2010. "Nonparametric comparison of regression functions," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 2039-2059, October.
    6. Sokbae (Simon) Lee & Yoon-Jae Whang, 2009. "Nonparametric tests of conditional treatment effects," CeMMAP working papers CWP36/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    7. Ian Christensen & Fuchun Li, 2013. "A Semiparametric Early Warning Model of Financial Stress Events," Staff Working Papers 13-13, Bank of Canada.
    8. Lapenta, Elia & Lavergne, Pascal, 2022. "Encompassing Tests for Nonparametric Regressions," TSE Working Papers 22-1332, Toulouse School of Economics (TSE).
    9. Gao, Jiti, 2007. "Nonlinear time series: semiparametric and nonparametric methods," MPRA Paper 39563, University Library of Munich, Germany, revised 01 Sep 2007.
    10. Khismatullina, Marina & Vogt, Michael, 2023. "Nonparametric comparison of epidemic time trends: The case of COVID-19," Journal of Econometrics, Elsevier, vol. 232(1), pages 87-108.
    11. Aureo de Paula & Xun Tang, 2020. "Testable Implications of Multiple Equilibria in Discrete Games with Correlated Types," Papers 2012.00787, arXiv.org.
    12. Gao, Jiti & King, Maxwell, 2003. "Estimation and model specification testing in nonparametric and semiparametric econometric models," MPRA Paper 11989, University Library of Munich, Germany, revised Feb 2006.
    13. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
    14. Jian Yan & Zhuoxi Li & Yang Ning & Yong Chen, 2025. "Machine-Learning-Assisted Comparison of Regression Functions," Papers 2510.24714, arXiv.org.
    15. Liangjun Su & Stefan Hoderlein & Halbert White, 2013. "Testing Monotonicity in Unobservables with Panel Data," Boston College Working Papers in Economics 892, Boston College Department of Economics, revised 01 Feb 2016.
    16. Wenceslao González-Manteiga & Rosa Crujeiras, 2013. "An updated review of Goodness-of-Fit tests for regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 361-411, September.
    17. 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.
    18. 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.
    19. Lyubchich, Vyacheslav & Gel, Yulia R., 2016. "A local factor nonparametric test for trend synchronism in multiple time series," Journal of Multivariate Analysis, Elsevier, vol. 150(C), pages 91-104.
    20. Sun, Yiguo, 2006. "A Consistent Nonparametric Equality Test Of Conditional Quantile Functions," Econometric Theory, Cambridge University Press, vol. 22(4), pages 614-632, August.
    21. Jian Yan & Zhuoxi Li & Xianyang Zhang, 2022. "Distance and Kernel-Based Measures for Global and Local Two-Sample Conditional Distribution Testing," Papers 2210.08149, arXiv.org, revised Aug 2025.
    22. Pascal Lavergne, 1998. "Selection of regressors in econometrics: parametric and nonparametric methods selection of regressors in econometrics," Econometric Reviews, Taylor & Francis Journals, vol. 17(3), pages 227-273.
    23. Liangjun Su & Xi Qu, 2017. "Specification Test for Spatial Autoregressive Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(4), pages 572-584, October.

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    JEL classification:

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

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