IDEAS home Printed from https://ideas.repec.org/p/arx/papers/0704.3686.html
   My bibliography  Save this paper

Improving Estimates of Monotone Functions by Rearrangement

Author

Listed:
  • Victor Chernozhukov

    (MIT)

  • Ivan Fernandez-Val

    (Boston University)

  • Alfred Galichon

    (Harvard University)

Abstract

Suppose that a target function is monotonic, namely, weakly increasing, and an original estimate of the target function is available, which is not weakly increasing. Many common estimation methods used in statistics produce such estimates. We show that these estimates can always be improved with no harm using rearrangement techniques: The rearrangement methods, univariate and multivariate, transform the original estimate to a monotonic estimate, and the resulting estimate is closer to the true curve in common metrics than the original estimate. We illustrate the results with a computational example and an empirical example dealing with age-height growth charts.

Suggested Citation

  • Victor Chernozhukov & Ivan Fernandez-Val & Alfred Galichon, 2007. "Improving Estimates of Monotone Functions by Rearrangement," Papers 0704.3686, arXiv.org, revised Nov 2010.
    • Handle: RePEc:arx:papers:0704.3686
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/0704.3686
    File Function: Latest version
    Download Restriction: no
    ---><---

    Other versions of this item:

    Citations

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


    Cited by:

    1. repec:pri:cepsud:223shephard is not listed on IDEAS
    2. 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.
    3. Birke, Melanie & Bissantz, Nicolai, 2007. "Shape constrained estimators in inverse regression models with convolution-type operator," Technical Reports 2007,35, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    4. Daniel J. Henderson & Christopher F. Parmeter, 2009. "Imposing economic constraints in nonparametric regression: survey, implementation, and extension," Advances in Econometrics, in: Nonparametric Econometric Methods, pages 433-469, Emerald Group Publishing Limited.
    5. Victor Chernozhukov & Iván Fernández-Val & Alfred Galichon, 2010. "Rearranging Edgeworth–Cornish–Fisher expansions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(2), pages 419-435, February.
    6. Andrew Shephard, 2017. "Equilibrium Search And Tax Credit Reform," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 58(4), pages 1047-1088, November.
    7. Holger Dette & Stanislav Volgushev, 2008. "Non‐crossing non‐parametric estimates of quantile curves," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(3), pages 609-627, July.
    8. Birke, Melanie, 2008. "Shape constrained kernel density estimation," Technical Reports 2008,08, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    9. Andrew Shephard, 2011. "Equilibrium Search and Tax Credit Reform," Working Papers 1336, Princeton University, Department of Economics, Center for Economic Policy Studies..
    10. Henderson, Daniel J. & List, John A. & Millimet, Daniel L. & Parmeter, Christopher F. & Price, Michael K., 2008. "Imposing Monotonicity Nonparametrically in First-Price Auctions," MPRA Paper 8769, University Library of Munich, Germany.
    11. Matthew J. Notowidigdo, 2011. "The Incidence of Local Labor Demand Shocks," 2011 Meeting Papers 629, Society for Economic Dynamics.

    More about this item

    Statistics

    Access and download statistics

    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:arx:papers:0704.3686. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.