标题： 稀疏估计量与oracle性质，或霍奇斯估计量的回归 显示英文标题

标题： Sparse Estimators and the Oracle Property, or the Return of Hodges' Estimator

摘要： 我们指出，Fan 和 Li（2001年、2002年、2004年）使用的关于oracle性质的概念存在一些问题，这些问题与 Hodges 估计量所涉及的众所周知的问题类似。 oracle性质通常是估计量稀疏性的结果。 我们证明，任何满足稀疏性性质的估计量，其最大风险都会收敛到损失函数的上确界；特别是，当损失函数无界时，最大风险会趋于无穷大。 为了便于阐述，该结果是在线性回归模型的框架下提出的，但其适用范围远远超出了这一设定。 在蒙特卡洛研究中，我们也评估了 Fan 和 Li（2001年）引入的平滑截断绝对偏差（SCAD）估计量在有限样本下的问题程度。 我们发现，该估计量在有限样本下的表现可能相当差，并且当该估计量被调整为稀疏性时，其相对于最大似然估计的最坏情况性能随着样本量的增加而恶化。 显示英文摘要

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.