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On Hodges' superefficiency and merits of oracle property in model selection

机译：在模型选择中霍奇格的超越和oracle属性的优点

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摘要

The oracle property of model selection procedures has attracted a large volume of favorable publications in the literature, but also faced criticisms of being ineffective and misleading in applications. Such criticisms, however, have appeared to be largely ignored by the majority of the popular statistical literature, despite their serious impact. In this paper, we present a new type of Hodges' estimators that can easily produce model selection procedures with the oracle and some other desired properties, but can be readily seen to perform poorly in parts of the parameter spaces that are fixed and independent of sample sizes. Consequently, the merits of the oracle property for model selection as extensively advocated in the literature are questionable and possibly overstated. In particular, because the mathematics employed in this paper are at an elementary level, this finding leads to new discoveries on the merits of the oracle property and exposes some overlooked crucial facts on model selection procedures.
机译：模型选择程序的Oracle属性在文献中吸引了大量有利的出版物，而且还面临批判在应用中无效和误导性。然而，尽管受到严重影响，但大多数受欢迎的统计文献似乎似乎很大程度上忽略了这种批评。在本文中，我们介绍了一种新型的Hodges估算器，可以轻松地使用Oracle和一些其他所需属性来生产模型选择程序，但可以很容易地看到在固定和独立于样本的参数空间的部分中执行不良大小。因此，在文献中广泛主张的模型选择的Oracle属性的优点是有疑的，并且可能夸大。特别是，由于本文所采用的数学是初级的，因此该发现导致了对Oracle财产的优点的新发现，并在模型选择程序上公布一些忽视的关键事实。

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