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Improving point and interval estimators of monotone functions by rearrangement

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  • V. Chernozhukov
  • I. Fernández-Val
  • A. Galichon

Abstract

Suppose that a target function is monotonic and an available original estimate of this target function is not monotonic. Rearrangements, univariate and multivariate, transform the original estimate to a monotonic estimate that always lies closer in common metrics to the target function. Furthermore, suppose an original confidence interval, which covers the target function with probability at least 1-α, is defined by an upper and lower endpoint functions that are not monotonic. Then the rearranged confidence interval, defined by the rearranged upper and lower endpoint functions, is monotonic, shorter in length in common norms than the original interval, and covers the target function with probability at least 1-α. We illustrate the results with a growth chart example. Copyright 2009, Oxford University Press.

Suggested Citation

  • 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.
  • Handle: RePEc:oup:biomet:v:96:y:2009:i:3:p:559-575
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    File URL: http://hdl.handle.net/10.1093/biomet/asp030
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    1. Matzkin, Rosa L., 1986. "Restrictions of economic theory in nonparametric methods," Handbook of Econometrics,in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 42, pages 2523-2558 Elsevier.
    2. Victor Chernozhukov & Ivan Fernandez-Val & Alfred Galichon, 2007. "Improving Estimates of Monotone Functions by Rearrangement," Papers 0704.3686, arXiv.org, revised Nov 2010.
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