论文标题
在高维Ornstein-uhlenbeck模型中漂移的Dantzig和Lasso估计器上
On Dantzig and Lasso estimators of the drift in a high dimensional Ornstein-Uhlenbeck model
论文作者
论文摘要
在本文中，我们为在稀疏性约束下的高维Ornstein-Uhlenbeck模型中的Dantzig和Lasso估计量提供了新的理论结果。我们的重点是相对于几个规范的估计器和误差界限的Oracle不等式。在套索估算器的背景下，我们的论文与[11]密切相关，[11]在行稀疏下研究了同样的问题。我们提高了它们的速率，并证明仅在模型上的基因性假设下证明了受限制的特征值性质。最后，我们展示了数值分析，以发现Dantzig和Lasso估计量的有限样本性能。
In this paper we present new theoretical results for the Dantzig and Lasso estimators of the drift in a high dimensional Ornstein-Uhlenbeck model under sparsity constraints. Our focus is on oracle inequalities for both estimators and error bounds with respect to several norms. In the context of the Lasso estimator our paper is strongly related to [11], who investigated the same problem under row sparsity. We improve their rates and also prove the restricted eigenvalue property solely under ergodicity assumption on the model. Finally, we demonstrate a numerical analysis to uncover the finite sample performance of the Dantzig and Lasso estimators.
