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

Jones, M. C. (2000). Rough-and-ready assessment of the degree and importance of smoothing in functional estimation. Statistica Neerlandica, 54(1) pp. 37–46.

DOI: https://doi.org/10.1111/1467-9574.00124

Abstract

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.

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