Improving Estimates of Monotone Functions by Rearrangement
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چکیده
Suppose that a target function f0 : R → R is monotonic, namely, weakly increasing, and an original estimate f̂ of the target function is available, which is not weakly increasing. Many common estimation methods used in statistics produce such estimates f̂ . 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 f̂∗, and the resulting estimate is closer to the true curve f0 in common metrics than the original estimate f̂ . We illustrate the results with a computational example and an empirical example dealing with age-height growth charts.
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تاریخ انتشار 2007