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Testing nonparametric shape restrictions

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  • Tatiana Komarova
  • Javier Hidalgo

Abstract

We describe and examine a test for a general class of shape constraints, such as constraints on the signs of derivatives, U-(S-)shape, symmetry, quasi-convexity, log-convexity, $r$-convexity, among others, in a nonparametric framework using partial sums empirical processes. We show that, after a suitable transformation, its asymptotic distribution is a functional of the standard Brownian motion, so that critical values are available. However, due to the possible poor approximation of the asymptotic critical values to the finite sample ones, we also describe a valid bootstrap algorithm.

Suggested Citation

  • Tatiana Komarova & Javier Hidalgo, 2019. "Testing nonparametric shape restrictions," Papers 1909.01675, arXiv.org, revised Jun 2020.
    • Handle: RePEc:arx:papers:1909.01675
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    References listed on IDEAS

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    1. Dette, Holger & Hoderlein, Stefan & Neumeyer, Natalie, 2016. "Testing multivariate economic restrictions using quantiles: The example of Slutsky negative semidefiniteness," Journal of Econometrics, Elsevier, vol. 191(1), pages 129-144.
    2. I. Gijbels & M. A. Ibrahim & A. Verhasselt, 2017. "Shape testing in quantile varying coefficient models with heteroscedastic error," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(2), pages 391-406, April.
    3. E. Mammen & C. Thomas‐Agnan, 1999. "Smoothing Splines and Shape Restrictions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 26(2), pages 239-252, June.
    4. Nikabadze, A. & Stute, W., 1997. "Model checks under random censorship," Statistics & Probability Letters, Elsevier, vol. 32(3), pages 249-259, March.
    5. V. Chernozhukov & I. Fernández-Val & A. Galichon, 2009. "Improving point and interval estimators of monotone functions by rearrangement," Biometrika, Biometrika Trust, vol. 96(3), pages 559-575.
    6. Diack, C.A.T. & Thomas-Agnan, C., 1996. "A Nonparametric Test of The Non-Convexity of Regression," Papers 976.427, Toulouse - GREMAQ.
    7. Hoderlein, Stefan & Su, Liangjun & White, Halbert & Yang, Thomas Tao, 2016. "Testing for monotonicity in unobservables under unconfoundedness," Journal of Econometrics, Elsevier, vol. 193(1), pages 183-202.
    8. Giacomini, Raffaella & Politis, Dimitris N. & White, Halbert, 2013. "A Warp-Speed Method For Conducting Monte Carlo Experiments Involving Bootstrap Estimators," Econometric Theory, Cambridge University Press, vol. 29(3), pages 567-589, June.
    9. Stefan Hoderlein & Liangjun Su & Halbert White & Thomas Tao Yang, 2016. "Testing for Monotonicity in Unobservables under Unconfoundedness," Working Papers 03-2016, Singapore Management University, School of Economics.
    10. Gerda Claeskens & Tatyana Krivobokova & Jean D. Opsomer, 2009. "Asymptotic properties of penalized spline estimators," Biometrika, Biometrika Trust, vol. 96(3), pages 529-544.
    11. Jo Thori Lind & Halvor Mehlum, 2010. "With or Without U? The Appropriate Test for a U‐Shaped Relationship," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 72(1), pages 109-118, February.
    12. Jason Abrevaya & Wei Jiang, 2005. "A Nonparametric Approach to Measuring and Testing Curvature," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 1-19, January.
    13. Chetverikov, Denis, 2019. "Testing Regression Monotonicity In Econometric Models," Econometric Theory, Cambridge University Press, vol. 35(4), pages 729-776, August.
    14. Lee, Jungyoon & Robinson, Peter M., 2016. "Series estimation under cross-sectional dependence," Journal of Econometrics, Elsevier, vol. 190(1), pages 1-17.
    15. Hong, Yongmiao & White, Halbert, 1995. "Consistent Specification Testing via Nonparametric Series Regression," Econometrica, Econometric Society, vol. 63(5), pages 1133-1159, September.
    16. Jungyoon Lee & Peter Robinson, 2016. "Series estimation under cross-sectional dependence," LSE Research Online Documents on Economics 63380, London School of Economics and Political Science, LSE Library.
    17. Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July.
    18. M. Ahkim & I. Gijbels & A. Verhasselt, 2017. "Shape testing in varying coefficient models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(2), pages 429-450, June.
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    Cited by:

    1. Zheng Fang, 2021. "A Unifying Framework for Testing Shape Restrictions," Papers 2107.12494, arXiv.org, revised Aug 2021.

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