摘要翻译：
研究了LASSO、SCAD和阈值估计在有限样本和大样本极限下的分布。在估计量被调谐到执行一致模型选择和估计量被调谐到执行保守模型选择的情况下，导出了渐近分布。我们的发现补充了Knight和Fu(2000)以及Fan和Li（2001）的发现。我们证明了无论估计量如何调整，分布通常都是高度非正态分布，并且这种性质在大样本中仍然存在。本文还得到了这些估计量的一致收敛速度，并证明了当估计量被调整以执行一致模型选择时，其收敛速度比1/根(n)慢。还提供了关于估计器的分布函数的估计的不可能结果。
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英文标题：
《On the Distribution of Penalized Maximum Likelihood Estimators: The
  LASSO, SCAD, and Thresholding》
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作者：
Benedikt M. Potscher, Hannes Leeb
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最新提交年份：
2009
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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：Machine Learning        机器学习
分类描述：Covers machine learning papers (supervised, unsupervised, semi-supervised learning, graphical models, reinforcement learning, bandits, high dimensional inference, etc.) with a statistical or theoretical grounding
覆盖机器学习论文（监督，无监督，半监督学习，图形模型，强化学习，强盗，高维推理等）与统计或理论基础
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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 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.
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PDF链接：
https://arxiv.org/pdf/711.066