标题： 具有潜在因子结构的亚组识别 显示英文标题

标题： Subgroup Identification with Latent Factor Structure

摘要： 亚组分析因其能够识别异质人群中有意义的亚组，从而增强预测能力，已经引起了越来越多的关注。然而，在社会科学和生物学等诸多领域，由于共同因素的影响，协变量之间往往高度相关。这种相关性对亚组识别提出了重大挑战，而这一问题在现有文献中常常被忽视。本文旨在通过在因子增强（稀疏）线性模型框架内提出一种中心增强的亚组识别方法，填补“发散维度”情境下的空白。该方法结合了降维与稀疏回归。我们提出的这种方法可以适应协变量之间的高交叉依赖性，并且相较于文献中传统的成对融合惩罚法（其复杂度为 $O(n^2)$），具有计算优势，其复杂度仅为 $O(nK)$，其中 $n$为样本量， $K$为子组数量。此外，我们在群心最小距离条件下的条件下研究了理想估计量的渐近性质。为了实现所提出的方法，我们引入了一种基于凸函数差的交替方向乘子法（DC-ADMM）算法，并证明其能在有限步内收敛到局部极小值。我们通过广泛的数值实验和一个真实的宏观经济数据实例展示了所提方法的优势。同时，一个实现该方法的 \texttt{R} 包 \texttt{SILFS} 已在CRAN上发布。 显示英文摘要

摘要： Subgroup analysis has garnered increasing attention for its ability to identify meaningful subgroups within heterogeneous populations, thereby enhancing predictive power. However, in many fields such as social science and biology, covariates are often highly correlated due to common factors. This correlation poses significant challenges for subgroup identification, an issue that is often overlooked in existing literature. In this paper, we aim to address this gap in the ``diverging dimension" regime by proposing a center-augmented subgroup identification method within the Factor Augmented (sparse) Linear Model framework. This method bridges dimension reduction and sparse regression. Our proposed approach is adaptable to the high cross-sectional dependence among covariates and offers computational advantages with a complexity of $O(nK)$, compared to the $O(n^2)$ complexity of the conventional pairwise fusion penalty method in the literature, where $n$ is the sample size and $K$ is the number of subgroups. We also investigate the asymptotic properties of the oracle estimators under conditions on the minimal distance between group centroids. To implement the proposed approach, we introduce a Difference of Convex functions-based Alternating Direction Method of Multipliers (DC-ADMM) algorithm and demonstrate its convergence to a local minimizer in a finite number of steps. We illustrate the superiority of the proposed method through extensive numerical experiments and a real macroeconomic data example. An \texttt{R} package, \texttt{SILFS}, implementing the method is also available on CRAN.