IDEAS home Printed from https://ideas.repec.org/p/zbw/sfb475/200649.html
   My bibliography  Save this paper

Testing strict monotonicity in nonparametric regression

Author

Listed:
  • Birke, Melanie
  • Dette, Holger

Abstract

A new test for strict monotonicity of the regression function is proposed which is based on a composition of an estimate of the inverse of the regression function with a common regression estimate. This composition is equal to the identity if and only if the ?true? regression function is strictly monotone, and a test based on an L2-distance is investigated. The asymptotic normality of the corresponding test statistic is established under the null hypothesis of strict monotonicity.

Suggested Citation

  • Birke, Melanie & Dette, Holger, 2006. "Testing strict monotonicity in nonparametric regression," Technical Reports 2006,49, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    • Handle: RePEc:zbw:sfb475:200649
    as

    Download full text from publisher

    File URL: https://www.econstor.eu/bitstream/10419/22693/1/tr49-06.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. J. O. Ramsay, 1998. "Estimating smooth monotone functions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(2), pages 365-375.
    2. Durot, Cécile, 2003. "A Kolmogorov-type test for monotonicity of regression," Statistics & Probability Letters, Elsevier, vol. 63(4), pages 425-433, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Birke, Melanie, 2006. "Central limit theorems for the integrated squared error of derivative estimators," Technical Reports 2006,53, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    2. Pramita Bagchi & Subhra Sankar Dhar, 2020. "A study on the least squares estimator of multivariate isotonic regression function," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(4), pages 1192-1221, December.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Eduardo L. Montoya & Wendy Meiring, 2016. "An F-type test for detecting departure from monotonicity in a functional linear model," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(2), pages 322-337, June.
    2. 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.
    3. 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.
    4. Zhang, Yu Yvette, 2017. "A shape constrained estimator of bidding function of first-price sealed-bid auctions," Economics Letters, Elsevier, vol. 150(C), pages 67-72.
    5. Wenchuan Liu & Yu Zhang & Qi Li, 2015. "A semiparametric varying coefficient model of monotone auction bidding processes," Empirical Economics, Springer, vol. 48(1), pages 313-335, February.
    6. Charu Sharma & Amber Habib & Sunil Bowry, 2018. "Cluster analysis of stocks using price movements of high frequency data from National Stock Exchange," Papers 1803.09514, arXiv.org.
    7. Shively, Thomas S. & Kockelman, Kara & Damien, Paul, 2010. "A Bayesian semi-parametric model to estimate relationships between crash counts and roadway characteristics," Transportation Research Part B: Methodological, Elsevier, vol. 44(5), pages 699-715, June.
    8. Zheng, Tingguo & Xiao, Han & Chen, Rong, 2015. "Generalized ARMA models with martingale difference errors," Journal of Econometrics, Elsevier, vol. 189(2), pages 492-506.
    9. Gattone, Stefano Antonio & Fortuna, Francesca & Evangelista, Adelia & Di Battista, Tonio, 2022. "Simultaneous confidence bands for the functional mean of convex curves," Econometrics and Statistics, Elsevier, vol. 24(C), pages 183-193.
    10. Brian Neelon & David B. Dunson, 2004. "Bayesian Isotonic Regression and Trend Analysis," Biometrics, The International Biometric Society, vol. 60(2), pages 398-406, June.
    11. Daniel R. Jiang & Warren B. Powell, 2015. "An Approximate Dynamic Programming Algorithm for Monotone Value Functions," Operations Research, INFORMS, vol. 63(6), pages 1489-1511, December.
    12. James P. Hughes & Patricia Totten, 2003. "Estimating the Accuracy of Polymerase Chain Reaction–Based Tests Using Endpoint Dilution," Biometrics, The International Biometric Society, vol. 59(3), pages 505-511, September.
    13. Christophe Abraham & Khader Khadraoui, 2015. "Bayesian regression with B-splines under combinations of shape constraints and smoothness properties," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 69(2), pages 150-170, May.
    14. repec:jss:jstsof:18:i04 is not listed on IDEAS
    15. 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.
    16. Christian Genest & Johanna G. Nešlehová, 2014. "A Conversation with James O. Ramsay," International Statistical Review, International Statistical Institute, vol. 82(2), pages 161-183, August.
    17. Hazelton, Martin L. & Turlach, Berwin A., 2011. "Semiparametric regression with shape-constrained penalized splines," Computational Statistics & Data Analysis, Elsevier, vol. 55(10), pages 2871-2879, October.
    18. Boudaoud, S. & Rix, H. & Meste, O., 2010. "Core Shape modelling of a set of curves," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 308-325, February.
    19. Jan Humplik & Gašper Tkačik, 2017. "Probabilistic models for neural populations that naturally capture global coupling and criticality," PLOS Computational Biology, Public Library of Science, vol. 13(9), pages 1-26, September.
    20. C Rohrbeck & D A Costain & A Frigessi, 2018. "Bayesian spatial monotonic multiple regression," Biometrika, Biometrika Trust, vol. 105(3), pages 691-707.
    21. N. G. Cadigan & J. Brattey, 2003. "Semiparametric Estimation of Tag Loss and Reporting Rates for Tag-Recovery Experiments Using Exact Time-at-Liberty Data," Biometrics, The International Biometric Society, vol. 59(4), pages 869-876, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:zbw:sfb475:200649. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ZBW - Leibniz Information Centre for Economics (email available below). General contact details of provider: https://edirc.repec.org/data/isdorde.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.