中文摘要：

作为二个流行地使用的可变选择方法， Dantzig 选购者和 LASSO 在一些情形被证明 asymptotically 相等。然而，它为线性模型一般来说不是事实，在 Gai 揭示了在 2013 的朱和 Lins 纸。在这份报纸，它进一步通常被看那 asymptotic 等价也不为有预言者的随机的设计的一个一般单个索引的模型是真的。达到这个目标，作者系统地为 Dantzig 选购者的历久不渝的模型选择调查必要、足够的条件。一个适应 Dantzig 选购者也为那些条件没满足的案例被推荐。另外，与为线性模型，的存在方法不同在错误术语的分布假设都不与预言者向量上的更紧的状况被假定的一宗交易被需要。小规模模拟被进行检验 Dantzig 选购者和适应 Dantzig 选购者的表演。

英文摘要：

As two popularly used variable selection methods, the Dantzig selector and the LASSO have been proved asymptotically equivalent in some scenarios. However, it is not the case in general for linear models, as disclosed in Gai, Zhu and Lin＇s paper in 2013. In this paper, it is further shown that generally the asymptotic equivalence is not true either for a general single-index model with random design of predictors. To achieve this goal, the authors systematically investigate necessary and sufficient conditions for the consistent model selection of the Dantzig selector. An adaptive Dantzig selector is also recommended for the cases where those conditions are not satisfied. Also, different from existing methods for linear models, no distributional assumption on error term is needed with a trade-off that more stringent condition on the predictor vector is assumed. A small scale simulation is conducted to examine the performances of the Dantzig selector and the adaptive Dantzig selector.