论文标题
Fréchet足够降低随机对象的尺寸
Fréchet Sufficient Dimension Reduction for Random Objects
论文作者
论文摘要
我们在本文中考虑了足够的尺寸降低，响应是公制空间中的复杂随机物体，并且欧几里得高度的预测因子。我们提出了一种新的方法，称为加权反回归集合方法，用于线性fréchet足够的尺寸降低。该方法被进一步推广为在繁殖内核希尔伯特空间中定义的新运算符，以减少非线性fréchet。我们通过渐近分析为新方法提供理论保证。密集的仿真研究验证了我们的建议的绩效。我们应用方法来分析手写数字数据以证明其在实际应用程序中的使用。
We in this paper consider Fréchet sufficient dimension reduction with responses being complex random objects in a metric space and high dimension Euclidean predictors. We propose a novel approach called weighted inverse regression ensemble method for linear Fréchet sufficient dimension reduction. The method is further generalized as a new operator defined on reproducing kernel Hilbert spaces for nonlinear Fréchet sufficient dimension reduction. We provide theoretical guarantees for the new method via asymptotic analysis. Intensive simulation studies verify the performance of our proposals. And we apply our methods to analyze the handwritten digits data to demonstrate its use in real applications.
