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Improving estimates of monotone functions by rearrangement

Author

Listed:
  • Victor Chernozhukov

    (Institute for Fiscal Studies and MIT)

  • Ivan Fernandez-Val

    (Institute for Fiscal Studies and Boston University)

  • Alfred Galichon

    (Institute for Fiscal Studies and NYU)

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," CeMMAP working papers CWP09/07, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    • Handle: RePEc:ifs:cemmap:09/07
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    File URL: http://cemmap.ifs.org.uk/wps/cwp0907.pdf
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    1. repec:pri:cepsud:223shephard is not listed on IDEAS
    2. 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.
    3. 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.
    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. 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. 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.
    7. Matthew J. Notowidigdo, 2020. "The Incidence of Local Labor Demand Shocks," Journal of Labor Economics, University of Chicago Press, vol. 38(3), pages 687-725.
    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, 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.
    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. 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.

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