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Improving Point and Interval Estimates of Monotone Functions by Rearrangement

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  • Victor Chernozhukov
  • Ivan Fernandez-Val
  • Alfred Galichon

Abstract

Suppose that a target function is monotonic, namely, weakly increasing, and an available original estimate of this target function is not weakly increasing. 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 simultaneous confidence interval, which covers the target function with probability at least $1-\alpha$, is defined by an upper and lower end-point functions that are not weakly increasing. Then the rearranged confidence interval, defined by the rearranged upper and lower end-point functions, is shorter in length in common norms than the original interval and also covers the target function with probability at least $1-\alpha$. We demonstrate the utility of the improved point and interval estimates with an age-height growth chart example.

Suggested Citation

  • Victor Chernozhukov & Ivan Fernandez-Val & Alfred Galichon, 2008. "Improving Point and Interval Estimates of Monotone Functions by Rearrangement," Papers 0806.4730, arXiv.org, revised Nov 2008.
  • Handle: RePEc:arx:papers:0806.4730
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