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摘要翻译：
我们指出了Fan and Li(2001，2002，2004)中与oracle属性概念有关的一些陷阱，这些陷阱使人想起与Hodges估计量有关的著名陷阱。oracle属性通常是估计器稀疏性的结果。我们证明了任何满足稀疏性的估计量收敛到损失函数上确界的风险最大；特别地，当损失函数为无界时，最大风险发散到无穷大。为了便于表示，结果是在线性回归模型的框架内设置的，但其泛化程度远远超出了该设置。在Monte Carlo研究中，我们还评估了Fan和Li(2001)中引入的光滑削波绝对偏差(SCAD)估计量在有限样本中的问题程度。我们发现该估计器在有限样本中的性能很差，当估计器调到稀疏度时，其最坏情况下相对于最大似然的性能随着样本大小的增加而恶化。
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英文标题：
《Sparse Estimators and the Oracle Property, or the Return of Hodges'
Estimator》
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作者：
Hannes Leeb, Benedikt M. Poetscher
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最新提交年份：
2007
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分类信息：
一级分类：Mathematics 数学
二级分类：Statistics Theory 统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Statistics 统计学
二级分类：Methodology 方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
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一级分类：Statistics 统计学
二级分类：Statistics Theory 统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
We point out some pitfalls related to the concept of an oracle property as used in Fan and Li (2001, 2002, 2004) which are reminiscent of the well-known pitfalls related to Hodges' estimator. The oracle property is often a consequence of sparsity of an estimator. We show that any estimator satisfying a sparsity property has maximal risk that converges to the supremum of the loss function; in particular, the maximal risk diverges to infinity whenever the loss function is unbounded. For ease of presentation the result is set in the framework of a linear regression model, but generalizes far beyond that setting. In a Monte Carlo study we also assess the extent of the problem in finite samples for the smoothly clipped absolute deviation (SCAD) estimator introduced in Fan and Li (2001). We find that this estimator can perform rather poorly in finite samples and that its worst-case performance relative to maximum likelihood deteriorates with increasing sample size when the estimator is tuned to sparsity.
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PDF链接：
https://arxiv.org/pdf/704.1466
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