A COMPARATIVE-STUDY OF SEVERAL SMOOTHING METHODS IN DENSITY-ESTIMATION
A COMPARATIVE-STUDY OF SEVERAL SMOOTHING METHODS IN DENSITY-ESTIMATION
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DOI：
10.1016/0167-9473(92)00066-z
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发表时间：
1994-02-01
影响因子：
1.8
通讯作者：
MANTEIGA, WG
中科院分区：
文献类型：
--
作者：
CAO, R;CUEVAS, A;MANTEIGA, WG
密度估计中的带宽选择理论发展很快。最近提出了几种方法（有大量的品种和子品种）作为最小二乘交叉验证的替代方案，多年来一直是标准。本文件包括：（a）对目前可用的主要方法进行最新的批判性审查。讨论提供了一些新的见解的重要问题，估计的最小化标准和引导基于方法的导频带宽的选择。(b)对10个选定带宽进行广泛的模拟研究。(c)最后的讨论与一些建议的从业人员。结论不容易用几句话概括，因为必须考虑不同的情况，必须指出重要的细微差别。然而，我们可以提到，一般来说，经典的交叉验证带宽表现出相对较差的行为（这对于伪似然方法尤其明显）。另一方面，虽然没有选择器看起来是一致更好的，但插件（与Sheather和Jones，J.皇家统计学家. B 5 1991）和（平滑的）基于Bootstrap的选择器显示出相当令人满意的性能，这表明它们可能成为密度估计中平滑问题的新标准方法。有趣的结果也得到了一种新的类型的带宽的基础上的拐点的数量。
The theory of bandwidth choice in density estimation is developing very fast. Several methods (with plenty of varieties and subvarieties) have been recently proposed as an alternative to least squares cross-validation, the standard for years. This paper includes (a) A critical up-to-date review of the main methods currently available. The discussion provide some new insights on the important problem of estimating the minimization criteria and on the choice of pilot bandwidths in bootstrap-based methods. (b) An extensive simulation study of ten selected bandwidths. (c) A final discussion with some recommendations for practitioners. The conclusions are not easily summarized in a few words, because different cases have to be considered and important nuances must be pointed out. However, we could mention that the classical cross-validation bandwidths show, generally speaking, a relatively poor behavior (this is especially clear for the pseudo-likelihood method). On the other hand, although no selector appears to be uniformly better, the plug-in (in a similar version to that proposed by Sheather and Jones, J. Royal Statist. Soc. Ser. B 5 1991) and the (smoothed) bootstrap-based selectors show a fairly satisfactory performance which suggests that they could be the new standard methods for the problem of smoothing in density estimation. Interesting results are also obtained for a new type of bandwidths based on the number of inflection points.