ON THE ADAPTIVE ELASTIC-NET WITH A DIVERGING NUMBER OF PARAMETERS.
ON THE ADAPTIVE ELASTIC-NET WITH A DIVERGING NUMBER OF PARAMETERS.
复制标题
DOI：
10.1214/08-aos625
复制
发表时间：
2009
影响因子：
4.5
通讯作者：
Zhang HH
中科院分区：
文献类型：
--
作者：
Zou H;Zhang HH
我们考虑了参数个数与样本大小不同的情况下的模型选择和估计问题。当维度较高时，理想的方法应该具有保证最优大样本性能的Oracle性质。此外，高维数据往往会产生共线性问题，这是理想方法需要妥善处理的问题。现有的许多变量选择方法不能同时达到这两个目标。本文提出了一种结合二次正则化和自适应加权套索收缩优点的自适应弹性网络。在弱正则条件下，建立了自适应弹性网的预言性。仿真结果表明，自适应弹性网在处理共线性问题上比其他类似Oracle的方法有更好的处理效果，从而提高了有限样本的性能。
We consider the problem of model selection and estimation in situations where the number of parameters diverges with the sample size. When the dimension is high, an ideal method should have the oracle property which ensures the optimal large sample performance. Furthermore, the high-dimensionality often induces the collinearity problem which should be properly handled by the ideal method. Many existing variable selection methods fail to achieve both goals simultaneously. In this paper, we propose the adaptive Elastic-Net that combines the strengths of the quadratic regularization and the adaptively weighted lasso shrinkage. Under weak regularity conditions, we establish the oracle property of the adaptive Elastic-Net. We show by simulations that the adaptive Elastic-Net deals with the collinearity problem better than the other oracle-like methods, thus enjoying much improved finite sample performance.