Sufficient dimension reduction often resorts to inverse regression, and most inverse regression methods rely on slicing a quantitative response. The choice of a particular slicing scheme is critical, but there are no current methods in the literature about how to select an optimal slicing scheme. We consider two popular slicing-based methods, namely, the sliced inverse regression and the sliced average variance estimation. By recasting the eigen-decomposition problem as a traceoptimization problem, we propose a penalized criterion for choosing an optimal slicing scheme. A dynamic programming algorithm is developed for numerical optimization. The theoretical properties are studied under mild conditions. Simulation examples show that our methods compare favorably with existing methods. An illustrative data analysis is also presented.

中文翻译：

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通过自适应切片降维

足够的降维通常求助于逆回归，而大多数逆回归方法依赖于对定量响应进行切片。特定切片方案的选择至关重要，但目前文献中没有关于如何选择最佳切片方案的方法。我们考虑两种流行的基于切片的方法，即切片逆回归和切片平均方差估计。通过将特征分解问题重铸为迹优化问题，我们提出了一个选择最佳切片方案的惩罚标准。动态规划算法被开发用于数值优化。理论性质在温和条件下进行研究。模拟示例表明，我们的方法与现有方法相比具有优势。还提供了说明性数据分析。