Liu Xiaoqian, Chi Eric C, Lange Kenneth
Department of Statistics, North Carolina State University.
Department of Statistics, Rice University.
Technometrics. 2023;65(1):117-126. doi: 10.1080/00401706.2022.2118172. Epub 2022 Oct 7.
Building on previous research of Chi and Chi (2022), the current paper revisits estimation in robust structured regression under the LE criterion. We adopt the majorization-minimization (MM) principle to design a new algorithm for updating the vector of regression coefficients. Our sharp majorization achieves faster convergence than the previous alternating proximal gradient descent algorithm (Chi and Chi, 2022). In addition, we reparameterize the model by substituting precision for scale and estimate precision via a modified Newton's method. This simplifies and accelerates overall estimation. We also introduce distance-to-set penalties to enable constrained estimation under nonconvex constraint sets. This tactic also improves performance in coefficient estimation and structure recovery. Finally, we demonstrate the merits of our improved tactics through a rich set of simulation examples and a real data application.
基于Chi和Chi（2022）之前的研究，本文重新审视了在LE准则下稳健结构化回归中的估计问题。我们采用主元最小化（MM）原理来设计一种更新回归系数向量的新算法。我们的精确主元化比之前的交替近端梯度下降算法（Chi和Chi，2022）收敛得更快。此外，我们通过用精度代替尺度对模型进行重新参数化，并通过改进的牛顿法估计精度。这简化并加速了整体估计。我们还引入了到集惩罚项，以实现非凸约束集下的约束估计。这种策略也提高了系数估计和结构恢复的性能。最后，我们通过一系列丰富的模拟示例和实际数据应用展示了我们改进策略的优点。
