Researchers have widely used exploratory factor analysis (EFA) to learn the latent structure underlying multivariate data. Rotation and regularised estimation are two classes of methods in EFA that they often use to find interpretable loading matrices. In this paper we propose a new family of oblique rotations based on component-wise $L^p$ loss functions $(0 < p\leq 1)$ that is closely related to an $L^p$ regularised estimator. We develop model selection and post-selection inference procedures based on the proposed rotation method. When the true loading matrix is sparse, the proposed method tends to outperform traditional rotation and regularised estimation methods in terms of statistical accuracy and computational cost. Since the proposed loss functions are nonsmooth, we develop an iteratively reweighted gradient projection algorithm for solving the optimisation problem. We also develop theoretical results that establish the statistical consistency of the estimation, model selection, and post-selection inference. We evaluate the proposed method and compare it with regularised estimation and traditional rotation methods via simulation studies. We further illustrate it using an application to the Big Five personality assessment.

翻译：研究人员广泛使用探索系数分析(EFA)来学习多变量数据背后的潜在结构。在全民教育中,轮换和定期估算是他们经常用来寻找可解释的装载矩阵的两类方法。在本文中,我们提议根据元件($L ⁇ p$)损失函数($(0 < p\leq1美元))进行新的倾斜旋转组合,该组合与美元固定估计值密切相关。我们根据拟议的轮换方法制定模型选择和选后推断程序。当真正的装载矩阵稀少时,拟议方法往往在统计准确性和计算成本方面超过传统的轮换和定期估算方法。由于拟议的损失函数不光滑,我们开发了解决优化问题的迭代再加权梯度预测算法。我们还开发了理论结果,以建立估算、模式选择和选后推算的统计一致性。我们评估了拟议方法,并通过模拟研究将其与常规估算和传统轮换方法进行比较。我们进一步说明它使用大五人格评估的应用。