论文标题

在线性模型中使用收缩的预测标准

Predictive Criteria for Prior Selection Using Shrinkage in Linear Models

论文作者

Dustin, Dean, Clarke, Bertrand, Clarke, Jennifer

论文摘要

可以通过从预先指定的罚款列表中选择惩罚或根据数据构建惩罚来选择收缩方法。如果给出了一类线性模型的惩罚列表,我们将根据样本量和基于数据扰动的预测稳定性标准下的样本量和非零参数的数量进行比较。这些比较为各种环境中的罚款选择提供了建议。如果偏好是为给定问题定制定制的惩罚,那么我们再次使用预测标准提出了一种基于遗传算法的技术。我们发现,总的来说,自定义罚款从未比任何常用的罚款都糟糕,但是在某些情况下,自定义罚款减少了可识别的罚款。由于惩罚选择在数学上等同于先前的选择,因此我们的方法还构建先验。 我们提供的技术和建议旨在用于有限样本案例。在这种情况下,我们认为在扰动下的预测稳定性是当不知道真实模型时可以调用的少数相关属性之一。然而,我们研究了在模拟中的变量包含,作为我们收缩选择策略的一部分,我们包括了Oracle财产注意事项。特别是,我们看到Oracle财产通常持有满足基本规律条件的罚款,因此不够限制,无法在罚款选择中发挥直接作用。此外,我们的真实数据示例还包括从模型错误指定合并的考虑因素。

Choosing a shrinkage method can be done by selecting a penalty from a list of pre-specified penalties or by constructing a penalty based on the data. If a list of penalties for a class of linear models is given, we provide comparisons based on sample size and number of non-zero parameters under a predictive stability criterion based on data perturbation. These comparisons provide recommendations for penalty selection in a variety of settings. If the preference is to construct a penalty customized for a given problem, then we propose a technique based on genetic algorithms, again using a predictive criterion. We find that, in general, a custom penalty never performs worse than any commonly used penalties but that there are cases the custom penalty reduces to a recognizable penalty. Since penalty selection is mathematically equivalent to prior selection, our method also constructs priors. The techniques and recommendations we offer are intended for finite sample cases. In this context, we argue that predictive stability under perturbation is one of the few relevant properties that can be invoked when the true model is not known. Nevertheless, we study variable inclusion in simulations and, as part of our shrinkage selection strategy, we include oracle property considerations. In particular, we see that the oracle property typically holds for penalties that satisfy basic regularity conditions and therefore is not restrictive enough to play a direct role in penalty selection. In addition, our real data example also includes considerations merging from model mis-specification.

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