利用重排改进单调函数的估计
Improving Estimates of Monotone Functions by Rearrangement
摘要：
假设目标函数是单调的，即弱增的，并且目标函数的原始估计是可用的，它不是弱增的。统计学中使用的许多常见估计方法都会产生这样的估计。我们表明，这些估计总是可以改进，没有伤害使用重排技术：重排方法，单变量和多变量，将原始估计转换为单调估计，并且所得估计在常见度量中比原始估计更接近真实曲线。我们用一个计算例子和一个处理年龄-身高增长图的经验例子来说明结果。
英文摘要：
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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