We consider variable selection in high-dimensional sparse multiresponse linear regression models, in which a q -dimensional response vector has a linear relationship with a p -dimensional covariate vector through a sparse coefficient matrix $$B\in R^{p\times q}$$ B ∈ R p × q . We propose a consistent procedure for the purpose of identifying the nonzeros in B . The procedure consists of two major steps, where the first step focuses on the detection of all the nonzero rows in B , the latter aims to further discover its individual nonzero cells. The first step is an extension of Orthogonal Matching Pursuit (OMP) and the second step adopts the bootstrap strategy. The theoretical property of our proposed procedure is established. Extensive numerical studies are presented to compare its performances with available representatives.

中文翻译：

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高维稀疏多响应线性回归模型中的变量选择

我们考虑高维稀疏多响应线性回归模型中的变量选择，其中 aq 维响应向量与 p 维协变量向量通过稀疏系数矩阵 $$B\in R^{p\times q}$ 具有线性关系$ B ∈ R p × q 。我们提出了一个一致的程序来识别 B 中的非零值。该过程包括两个主要步骤，其中第一步侧重于检测 B 中的所有非零行，后者旨在进一步发现其各个非零单元格。第一步是正交匹配追踪（OMP）的扩展，第二步采用引导策略。我们提出的程序的理论属性已经建立。提供了广泛的数值研究，以将其性能与可用的代表进行比较。