Improving Point and Interval Estimates of Monotone Functions by Rearrangement

Victor Chernozhukov, Ivan Fernandez-Val () and 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 $1-\alpha$, 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.

Date: 2008-06, Revised 2008-11
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Published in Biometrika (2009) 96 (3): 559-575

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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 estimators of monotone functions by rearrangement (2009)
Working Paper: Improving point and interval estimates of monotone functions by rearrangement (2008)
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