On the distribution of penalized maximum likelihood estimators: The LASSO, SCAD, and thresholding
On the distribution of penalized maximum likelihood estimators: The LASSO, SCAD, and thresholding
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DOI：
10.1016/j.jmva.2009.06.010
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发表时间：
2009-10-01
影响因子：
1.6
通讯作者：
Leeb, Hannes
中科院分区：
文献类型：
--
作者：
Poetscher, Benedikt M.;Leeb, Hannes
我们研究的分布的LASSO，SCAD和阈值估计，在有限样本和大样本限制。渐近分布的情况下，估计量进行调整，以执行一致的模型选择和估计量进行调整，以执行保守的模型选择。我们的发现补充了Knight和Fu [K. Knight，W.傅，Lasso型估计的渐近性，统计年鉴28（2000）1356-1378]和范和李[J.范，R. Li，Variable selection via non-convex penalized likelihood and its oracle properties，Journal of the American Statistical Association 96（2001）1348-1360]。我们发现，无论估计量如何调整，分布通常都是高度非正态的，并且这种特性在大样本中仍然存在。同时也得到了这类估计的一致收敛速度，并且证明了在模型选择一致的情况下，这类估计的一致收敛速度比n（-1/2）慢。(C)2009 Elsevier Inc. All rights reserved.
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 [K. Knight, W. Fu, Asymptotics for lasso-type estimators, Annals of Statistics 28 (2000) 1356-1378] and Fan and Li [J. Fan, R. Li, Variable selection via non-concave penalized likelihood and its oracle properties, journal of the American Statistical Association 96 (2001) 1348-1360]. We show that the distributions are typically highly non-normal 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 n(-1/2) in case the estimator is tuned to perform consistent model selection, An impossibility result regarding estimation of the estimators' distribution function is also provided. (C) 2009 Elsevier Inc. All rights reserved.