High-dimensional data analysis using traditional models suffers from overparameterization. Two types of techniques are commonly used to reduce the number of parameters - regularization and dimension reduction. In this project, we combine them by imposing a sparse factor structure and propose a regularized estimator to further reduce the number of parameters in factor models. A challenge limiting the widespread application of factor models is that factors are hard to interpret, as both factors and the loading matrix are unobserved. To address this, we introduce a penalty term when estimating the loading matrix for a sparse estimate. As a result, each factor only drives a smaller subset of time series that exhibit the strongest correlation, improving the factor interpretability. The theoretical properties of the proposed estimator are investigated. The simulation results are presented to confirm that our algorithm performs well. We apply our method to Hawaii tourism data.

翻译：传统模型在高维数据分析中面临过度参数化问题。为减少参数数量，通常采用正则化与降维两类技术。本项目通过引入稀疏因子结构将二者结合，提出一种正则化估计量以进一步降低因子模型中的参数数量。限制因子模型广泛应用的一个挑战在于因子难以解释，因为因子与载荷矩阵均不可观测。为解决此问题，我们在估计载荷矩阵时引入惩罚项以获得稀疏估计。由此，每个因子仅驱动具有最强相关性的较小时间序列子集，从而提升因子的可解释性。本文研究了所提估计量的理论性质，并通过仿真结果验证了算法的良好性能。最后，我们将该方法应用于夏威夷旅游数据。