High-dimensional generalizations of asymmetric least squares regression and their applications
非对称最小二乘回归的高维推广及其应用AI 解读 ↓
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非对称最小二乘回归的高维推广及其应用
- 研究问题
- 如何在高维数据中实施稀疏非对称最小二乘回归，并区分影响条件均值与条件尺度的变量，允许两组变量重叠？
- 方法与思路
- 作者提出采用 Lasso 或非凸惩罚的 SALES 及耦合版本 COSALES，开发统一算法，并研究理论性质与异方差检测。
- 材料陈述的贡献
- 摘要称，使用 SCAD 或 MCP 的 COSALES 可一致识别均值与尺度的重要变量集合，即使二者重叠，并展示模拟和实证表现。
- 阅读关注点
- 应核对耦合模型如何区分均值与尺度、变量选择一致性的条件、算法收敛，以及与稀疏分位数回归的比较设计。
- 阅读边界
- 仅据版本未注明的 OpenAlex 摘要；理论条件、调参方式及模拟和真实数据结果未具体给出，不能认定全面优于其他方法。
原文摘要
Asymmetric least squares regression is an important method that has wide applications in statistics, econometrics and finance. The existing work on asymmetric least squares only considers the traditional low dimension and large sample setting. In this paper, we systematically study the Sparse Asymmetric LEast Squares (SALES) regression under high dimensions where the penalty functions include the Lasso and nonconvex penalties. We develop a unified efficient algorithm for fitting SALES and establish its theoretical properties. As an important application, SALES is used to detect heteroscedasticity in high-dimensional data. Another method for detecting heteroscedasticity is the sparse quantile regression. However, both SALES and the sparse quantile regression may fail to tell which variables are important for the conditional mean and which variables are important for the conditional scale/variance, especially when there are variables that are important for both the mean and the scale. To that end, we further propose a COupled Sparse Asymmetric LEast Squares (COSALES) regression which can be efficiently solved by an algorithm similar to that for solving SALES. We establish theoretical properties of COSALES. In particular, COSALES using the SCAD penalty or MCP is shown to consistently identify the two important subsets for the mean and scale simultaneously, even when the two subsets overlap. We demonstrate the empirical performance of SALES and COSALES by simulated and real data.