标题： 关于惩罚最大似然估计量的分布：LASSO、SCAD和阈值化 显示英文标题

标题： On the Distribution of Penalized Maximum Likelihood Estimators: The LASSO, SCAD, and Thresholding

摘要： 我们研究了LASSO、SCAD和阈值估计量的分布，在有限样本和大样本极限下都进行了分析。 对于这两种情况——其中一种是估计量被调整以实现一致模型选择，另一种是调整以实现保守模型选择——得到了渐近分布的结果。我们的发现补充了Knight和Fu（2000）以及Fan和Li（2001）的研究成果。 我们表明，无论估计量如何调整，这些分布通常高度非正态，并且这种性质在大样本情况下仍然存在。还得到了这些估计量的一致收敛速度，当估计量被调整以实现一致模型选择时，该速度被证明慢于1/√n。此外，还提供了一个关于无法估计这些估计量分布函数的结果。 显示英文摘要

摘要： We study the distributions of the LASSO, SCAD, and thresholding estimators, in finite samples and in the large-sample limit. The asymptotic distributions are derived for both the case where the estimators are tuned to perform consistent model selection and for the case where the estimators are tuned to perform conservative model selection. Our findings complement those of Knight and Fu (2000) and Fan and Li (2001). We show that the distributions are typically highly nonnormal regardless of how the estimator is tuned, and that this property persists in large samples. The uniform convergence rate of these estimators is also obtained, and is shown to be slower than 1/root(n) in case the estimator is tuned to perform consistent model selection. An impossibility result regarding estimation of the estimators' distribution function is also provided.