论文标题
通过主要不对称最小二乘尺寸降低足够的尺寸
On sufficient dimension reduction via principal asymmetric least squares
论文作者
论文摘要
在本文中，我们将主要的不对称最小二乘（PAL）作为线性和非线性降低尺寸降低的统一框架。经典方法，例如切片的反回归（Li，1991）和主要支持向量机（Li，Artemiou和Li，2011年），在存在异质性的情况下可能表现不佳，而我们的建议通过综合不同的预期水平来解决此限制。通过广泛的数值研究，我们证明了在计算时间和估计准确性方面，PAL的表现出色。为了对PAL的渐近分析进行线性降低，我们开发了新的工具来计算非lipschitz函数的期望的导数。
In this paper, we introduce principal asymmetric least squares (PALS) as a unified framework for linear and nonlinear sufficient dimension reduction. Classical methods such as sliced inverse regression (Li, 1991) and principal support vector machines (Li, Artemiou and Li, 2011) may not perform well in the presence of heteroscedasticity, while our proposal addresses this limitation by synthesizing different expectile levels. Through extensive numerical studies, we demonstrate the superior performance of PALS in terms of both computation time and estimation accuracy. For the asymptotic analysis of PALS for linear sufficient dimension reduction, we develop new tools to compute the derivative of an expectation of a non-Lipschitz function.
