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A Kolmogorov-type test for monotonicity of regression

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  • Durot, Cécile

Abstract

A new nonparametric procedure for testing monotonicity of a regression mean is proposed. The test is shown to have prescribed asymptotic level and good asymptotic power. It is based on the supremum distance from an empirical process to its least concave majorant and is very easily implementable. A simulation study is reported to demonstrate finite sample behavior of the procedure.

Suggested Citation

  • Durot, Cécile, 2003. "A Kolmogorov-type test for monotonicity of regression," Statistics & Probability Letters, Elsevier, vol. 63(4), pages 425-433, July.
    • Handle: RePEc:eee:stapro:v:63:y:2003:i:4:p:425-433
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    Citations

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    Cited by:

    1. Zheng Fang & Juwon Seo, 2021. "A Projection Framework for Testing Shape Restrictions That Form Convex Cones," Econometrica, Econometric Society, vol. 89(5), pages 2439-2458, September.
    2. Misha Beek & Hennie Daniels, 2014. "A Non-parametric Test for Partial Monotonicity in Multiple Regression," Computational Economics, Springer;Society for Computational Economics, vol. 44(1), pages 87-100, June.
    3. Vladimir N. Kulikov & Hendrik P. Lopuhaä, 2008. "Distribution of Global Measures of Deviation Between the Empirical Distribution Function and Its Concave Majorant," Journal of Theoretical Probability, Springer, vol. 21(2), pages 356-377, June.
    4. Fadoua Balabdaoui & Cécile Durot & Hanna Jankowski, 2023. "Behaviour of the Monotone Single Index Model Under Repeated Measurements," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 324-350, February.
    5. Simone Fiori, 2013. "An isotonic trivariate statistical regression method," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 7(2), pages 209-235, June.
    6. Gutknecht, Daniel, 2016. "Testing for monotonicity under endogeneity," Journal of Econometrics, Elsevier, vol. 190(1), pages 100-114.
    7. repec:dau:papers:123456789/9451 is not listed on IDEAS
    8. Delgado, Miguel A. & Escanciano, Juan Carlos, 2012. "Distribution-free tests of stochastic monotonicity," Journal of Econometrics, Elsevier, vol. 170(1), pages 68-75.
    9. Denis Chetverikov, 2012. "Testing regression monotonicity in econometric models," CeMMAP working papers CWP35/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    10. Lee, Sokbae & Song, Kyungchul & Whang, Yoon-Jae, 2013. "Testing functional inequalities," Journal of Econometrics, Elsevier, vol. 172(1), pages 14-32.
    11. Daniel Gutknecht, 2013. "Testing for Monotonicity under Endogeneity An Application to the Reservation Wage Function," Economics Series Working Papers 673, University of Oxford, Department of Economics.
    12. Miguel A. Delgado & Juan Carlos Escanciano, 2013. "Conditional Stochastic Dominance Testing," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(1), pages 16-28, January.
    13. Ted Westling & Peter Gilbert & Marco Carone, 2020. "Causal isotonic regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(3), pages 719-747, July.
    14. Birke, Melanie & Dette, Holger, 2006. "Testing strict monotonicity in nonparametric regression," Technical Reports 2006,49, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    15. Colubi, Ana & Domínguez-Menchero, J. Santos & González-Rodríguez, Gil, 2014. "Testing constancy in monotone response models," Computational Statistics & Data Analysis, Elsevier, vol. 72(C), pages 45-56.
    16. Melanie Birke & Natalie Neumeyer, 2013. "Testing Monotonicity of Regression Functions – An Empirical Process Approach," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(3), pages 438-454, September.

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