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Improving estimates of monotone functions by rearrangement

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  • Victor Chernozhukov

    () (Institute for Fiscal Studies and Massachusetts Institute of Technology)

  • Ivan Fernandez-Val
  • Alfred Galichon

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.

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File URL: http://cemmap.ifs.org.uk/wps/cwp0907.pdf
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Bibliographic Info

Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP09/07.

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Date of creation: Apr 2007
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Handle: RePEc:ifs:cemmap:09/07

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Cited by:
  1. Victor Chernozhukov & Iván Fernández-Val & Alfred Galichon, 2010. "Rearranging Edgeworth–Cornish–Fisher expansions," Economic Theory, Springer, vol. 42(2), pages 419-435, February.
  2. 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.
  3. Matthew J. Notowidigdo, 2011. "The Incidence of Local Labor Demand Shocks," NBER Working Papers 17167, National Bureau of Economic Research, Inc.
  4. Victor Chernozhukov & Ivan Fernandez-Val & Alfred Galichon, 2008. "Improving point and interval estimates of monotone functions by rearrangement," CeMMAP working papers CWP17/08, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  5. Henderson, Daniel J. & Parmeter, Christopher F., 2009. "Imposing Economic Constraints in Nonparametric Regression: Survey, Implementation and Extension," IZA Discussion Papers 4103, Institute for the Study of Labor (IZA).
  6. 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.
  7. Birke, Melanie, 2008. "Shape constrained kernel density estimation," Technical Reports 2008,08, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
  8. Andrew Shephard, 2011. "Equilibrium Search and Tax Credit Reform," Working Papers 1336, Princeton University, Department of Economics, Center for Economic Policy Studies..

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