Adaptively weighted group Lasso for semiparametric quantile regression models
Adaptively weighted group Lasso for semiparametric quantile regression models
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DOI：
10.3150/18-bej1091
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发表时间：
2019-11
期刊：
影响因子：
1.5
通讯作者：
Toshio Honda;C. Ing;Wei-Ying Wu
中科院分区：
文献类型：
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作者：
Toshio Honda;C. Ing;Wei-Ying Wu
针对变系数分位数回归模型和具有超高维协变量的加性分位数回归模型，提出了一种同时进行变量选择和结构识别的自适应加权群Lasso方法.在一个强稀疏性条件下，我们建立了建议的Lasso过程的选择一致性时，其中的权重满足一组一般条件。然而，该一致性结果依赖于用于Lasso惩罚的调谐参数的合适选择，这在实践中可能难以实现。为了减轻这一困难，我们提出了一个BIC型标准，我们称之为高维信息标准（HDIC），并表明，建议的Lasso程序与HDIC确定的调谐参数仍然实现选择一致性。我们的模拟研究有力地支持了我们的理论研究结果。
We propose an adaptively weighted group Lasso procedure for simultaneous variable selection and structure identification for varying coefficient quantile regression models and additive quantile regression models with ultra-high dimensional covariates. Under a strong sparsity condition, we establish selection consistency of the proposed Lasso procedure when the weights therein satisfy a set of general conditions. This consistency result, however, is reliant on a suitable choice of the tuning parameter for the Lasso penalty, which can be hard to make in practice. To alleviate this difficulty, we suggest a BIC-type criterion, which we call high-dimensional information criterion (HDIC), and show that the proposed Lasso procedure with the tuning parameter determined by HDIC still achieves selection consistency. Our simulation studies support strongly our theoretical findings.