Improving Estimates of Monotone Functions by Rearrangement

Details Improving Estimates of Monotone Functions by Rearrangement Improving Estimates of Monotone Functions by Rearrangement

2007-04-27

arxiv.org/abs/0704.3686v2

Statistics

Methodology

31 pages, 8 figures, low resolution figures. This paper has been withdraw by the authors because it has been replaced by "Impr

Scientific paper

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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