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Improving estimates of monotone functions by rearrangement

Authors: Victor Chernozhukov , Ivan Fernandez-Val and Alfred Galichon
Date: 01 September 2009
Type: Journal Article, Biometrika, Vol. 96, No. 3, pp. 559 - 575
DOI: 10.1093/biomet/asp030

Abstract

Suppose that a target function is monotonic, namely, weakly increasing, and an original estimate of the target function is available, which is not weakly increasing. Many common estimation methods used in statistics produce such estimates. We show that these estimates can always be improved with no harm using rearrangement techniques: The rearrangement methods, univariate and multivariate, transform the original estimate to a monotonic estimate, and the resulting estimate is closer to the true curve in common metrics than the original estimate. We illustrate the results with a computational example and an empirical example dealing with age-height growth charts.

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Previous version:
Victor Chernozhukov, Ivan Fernandez-Val and Alfred Galichon July 2008, Improving point and interval estimates of monotone functions by rearrangement, cemmap Working Paper, CWP17/08
Victor Chernozhukov, Ivan Fernandez-Val and Alfred Galichon April 2007, Improving estimates of monotone functions by rearrangement, cemmap Working Paper, CWP09/07

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