Improving point and interval estimators of monotone functions by rearrangement

Victor Chernozhukov, Ivan Fernandez-Val () and Alfred Galichon ()
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Alfred Galichon: ECON - Département d'économie (Sciences Po) - Sciences Po - Sciences Po - CNRS - Centre National de la Recherche Scientifique

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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.

Date: 2009
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Citations: View citations in EconPapers (10)

Published in Biometrical Journal, 2009, 96 (3), pp.559 - 575. ⟨10.1093/biomet/asp030⟩

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Related works:
Journal Article: Improving point and interval estimators of monotone functions by rearrangement (2009)
Working Paper: Improving point and interval estimators of monotone functions by rearrangement (2009)
Working Paper: Improving Point and Interval Estimates of Monotone Functions by Rearrangement (2008)
Working Paper: Improving point and interval estimates of monotone functions by rearrangement (2008)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:spmain:hal-03596970

DOI: 10.1093/biomet/asp030

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