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Rough-and-ready assessment of the degree and importance of smoothing in functional estimation

机译:粗略评估功能估计中平滑的程度和重要性

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摘要

In nonparametric estimation of functionals of a distribution, it may or may not be desirable, or indeed necessary, to introduce a degree of smoothing into this estimation. In this article, I describe a method for assessing, with just a little thought about the functional of interest, (i) whether smoothing is likely to prove worthwhile, and (ii) if so, roughly how much smoothing is appropriate (in order-of-magnitude terms). This rule-of-thumb is not guaranteed to be accurate nor does it give a complete answer to the smoothing problem. However, I have found it very useful over a number of years; many examples of its use, and limitations, are given.
机译:在分布的泛函的非参数估计中,将平滑度引入此估计中可能会或可能不会,也可能确实是必要的。在本文中,我描述了一种评估方法,仅需考虑一下感兴趣的功能,(i)平滑是否有可能值得证明,以及(ii)如果这样,大致可以进行多少平滑(顺序为-量级项)。这种经验法则不能保证准确,也不能为平滑问题提供完整的答案。但是,多年来我发现它非常有用。给出了许多使用和限制的示例。

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