MODEL INDEXING AND SMOOTHING PARAMETER SELECTION IN NONPARAMETRIC FUNCTION ESTIMATION
MODEL INDEXING AND SMOOTHING PARAMETER SELECTION IN NONPARAMETRIC FUNCTION ESTIMATION
复制标题
非参数函数估计中的模型索引和平滑参数选择
DOI：
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发表时间：
1998
期刊：
影响因子：
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通讯作者：
Chong Gu
中科院分区：
文献类型：
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作者：
Chong Gu
平滑参数选择是非参数函数估计中研究最深入的课题之一。然而，现有文献很大程度上忽略了一个密切相关的问题，即确定平滑参数的适当指数。通过启发式论证和简单的模拟，我们表明大多数当前的工作指数在概念上是“不正确的”，因为它们在重复实验中无法跨重复解释。因此，一些流行的工作概念，例如预期均方误差和“自由度”，在仔细审查下似乎很脆弱。由于技术限制，这些论点主要是在惩罚似然设置中展开的，但概念上的相似之处也可以与其他设置进行比较。根据我们的发现，还进行了模拟和讨论，以比较简单交叉验证方法与用于平滑参数选择的更复杂插件方法的相对优点，并探讨相关问题。这一发展源于试图理解最优平滑参数与交叉验证平滑参数之间广为人知的负相关性，但事实证明这种负相关性几乎没有统计相关性。
Smoothing parameter selection is among the most intensively studied subjects in nonparametric function estimation. A closely related issue, that of iden- tifying a proper index for the smoothing parameter, is however largely neglected in the existing literature. Through heuristic arguments and simple simulations, we show that most current working indices are conceptually "incorrect", in the sense that they are not interpretable across-replicate in repeated experiments. As a con sequence, a few popular working concepts, such as expected mean square error and "degrees of freedom", appear vulnerable under close scrutiny. Due to tech- nical constraints, the arguments are mainly developed in the penalized likelihood setting, but conceptual parallels can be drawn to other settings as well. In the light of our findings, simulations and discussion are also presented to compare the relative merits of the simple cross-validation method versus the more sophisticated plug-in method for smoothing parameter selection, and to explore related issues. The development stems from an attempt to understand the well-publicized nega- tive correlation between optimal and cross-validation smoothing parameters, which however turns out to bear little statistical relevance.