Improving Point and Interval Estimates of Monotone Functions by Rearrangement

Victor Chernozhukov; Ivan Fernandez-Val; Alfred Galichon

doi:10.1093/biomet/asp030

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arXiv · 0806.4730

Improving Point and Interval Estimates of Monotone Functions by Rearrangement

Victor Chernozhukov·Ivan Fernandez-Val·Alfred Galichon

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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 $1-α$, 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 $1-α$. We demonstrate the utility of the improved point and interval estimates with an age-height growth chart example.

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BibTeX RIS

Victor Chernozhukov, Ivan Fernandez-Val, Alfred Galichon. 2008-11-07. Improving Point and Interval Estimates of Monotone Functions by Rearrangement. https://doi.org/10.1093/biomet%2Fasp030

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