论文标题
具有内部包膜的多元回归中的半参数有效尺寸降低
Semiparametric Efficient Dimension Reduction in multivariate regression with an Inner Envelope
论文作者
论文摘要
最近，苏和库克提出了一种称为内膜的尺寸缩小技术，该技术比原始的包络或现有缩小尺寸缩小技术要高得多，用于多元回归。但是，他们的技术依赖于具有正态分布错误的线性模型，这在实践中可能会违反。在这项工作中，我们提出了内膜的半参数变体，该变体不依赖线性模型或正态性假设。我们表明，我们的提案导致内部包膜空间的全球和本地效率估计器。我们还提出了一种可计算上的算法，以估计内部包膜。我们的模拟和实际数据分析表明，与在各种设置中的现有缩小方法相比，我们的方法既有稳健又有效。
Recently, Su and Cook proposed a dimension reduction technique called the inner envelope which can be substantially more efficient than the original envelope or existing dimension reduction techniques for multivariate regression. However, their technique relied on a linear model with normally distributed error, which may be violated in practice. In this work, we propose a semiparametric variant of the inner envelope that does not rely on the linear model nor the normality assumption. We show that our proposal leads to globally and locally efficient estimators of the inner envelope spaces. We also present a computationally tractable algorithm to estimate the inner envelope. Our simulations and real data analysis show that our method is both robust and efficient compared to existing dimension reduction methods in a diverse array of settings.
