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Improving point and interval estimators of monotone functions by rearrangement

Author

Listed:
  • Victor Chernozhukov
  • Ivan Fernandez-Val
  • Alfred Galichon

    (ECON - Département d'économie (Sciences Po) - Sciences Po - Sciences Po - CNRS - Centre National de la Recherche Scientifique)

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.

Suggested Citation

  • Victor Chernozhukov & Ivan Fernandez-Val & Alfred Galichon, 2009. "Improving point and interval estimators of monotone functions by rearrangement," SciencePo Working papers Main hal-03596970, HAL.
  • Handle: RePEc:hal:spmain:hal-03596970
    DOI: 10.1093/biomet/asp030
    Note: View the original document on HAL open archive server: https://hal-sciencespo.archives-ouvertes.fr/hal-03596970
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    References listed on IDEAS

    as
    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," CeMMAP working papers CWP09/07, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
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