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摘要翻译：
研究了稀疏高维线性回归模型中协变量个数随样本量增加时SCAD惩罚最小二乘估计的渐近性质。我们特别感兴趣的是使用这个估计器同时进行变量选择和估计。我们证明了在适当的条件下，SCAD惩罚的最小二乘估计对于变量选择是相合的，并且非零系数的估计具有与预先知道零系数时相同的渐近分布。仿真研究表明，该估计器在变量选择和估计方面具有良好的性能。
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英文标题：
《Asymptotic oracle properties of SCAD-penalized least squares estimators》
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作者：
Jian Huang, Huiliang Xie
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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：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 asymptotic properties of the SCAD-penalized least squares estimator in sparse, high-dimensional, linear regression models when the number of covariates may increase with the sample size. We are particularly interested in the use of this estimator for simultaneous variable selection and estimation. We show that under appropriate conditions, the SCAD-penalized least squares estimator is consistent for variable selection and that the estimators of nonzero coefficients have the same asymptotic distribution as they would have if the zero coefficients were known in advance. Simulation studies indicate that this estimator performs well in terms of variable selection and estimation.
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PDF链接：
https://arxiv.org/pdf/709.0863
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