Adaptive Lasso for sparse high-dimensional regression models
Adaptive Lasso for sparse high-dimensional regression models
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DOI：
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发表时间：
2008-10
影响因子：
1.4
通讯作者：
Jian Huang;Shuangge Ma;Cun-Hui Zhang
中科院分区：
文献类型：
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作者：
Jian Huang;Shuangge Ma;Cun-Hui Zhang
研究了协变量个数随样本量增加时，稀疏高维线性回归模型中自适应Lasso估计的渐近性质。我们考虑使用自适应套索进行变量选择，其中惩罚中的L1范数通过依赖于数据的权重进行重新加权。我们证明了，如果有一个合理的初始估计，在适当的条件下，自适应Lasso以概率收敛到1的概率正确地选择了非零系数的协变量，并且非零系数的估计量具有与预先知道零系数时相同的渐近分布。从而得到了Fan和Li(2001)和Fan和Peng(2004)意义下的适应性Lasso Hasan Oracle性质。此外，在系数为零的协变量与系数为非零的协变量弱相关的部分正交性条件下，可以利用边际回归得到初始估计。有了这个初始估计，即使协变量的数目远远大于样本大小，自适应Lasso仍然具有Oracle性质。
We study the asymptotic properties of the adaptive Lasso estimators in sparse, high-dimensional, linear regression models when the number of covariates may increase with the sample size. We consider variable selection using the adap- tive Lasso, where the L1 norms in the penalty are re-weighted by data-dependent weights. We show that, if a reasonable initial estimator is available, under ap- propriate conditions, the adaptive Lasso correctly selects covariates with nonzero coefficients with probability converging to one, and that theestimators of nonzero coefficients have the same asymptotic distribution they would have if the zero co- efficients were known in advance. Thus, the adaptive Lasso hasan oracle property in the sense of Fan and Li (2001) and Fan and Peng (2004). In addition, under a partial orthogonality condition in which the covariates with zero coefficients are weakly correlated with the covariates with nonzero coefficients, marginal regression can be used to obtain the initial estimator. With this initial estimator, the adaptive Lasso has the oracle property even when the number of covariates is much larger than the sample size.