论文标题
非参数回归的置信区间
Confidence intervals for nonparametric regression
论文作者
论文摘要
从拉德马赫理论的角度来看，我们证明并讨论了回归方案成本具有一般损失函数的概率的非沉淀范围，以及对于平均$ l^{2} $的最佳性，从平均$ l^{2} $ - 与Vapnik-Chervnik-Chervonenkis理论的平均有条件期望回归的基本有条件期望的距离。 结果来自涉及独立但可能是非组织培训样本的分析，并且可以以我们解释和说明的方式扩展到培训样本表现出依赖性的相关情况。
We demonstrate and discuss nonasymptotic bounds in probability for the cost of a regression scheme with a general loss function from the perspective of the Rademacher theory, and for the optimality with respect to the average $L^{2}$-distance to the underlying conditional expectations of least squares regression outcomes from the perspective of the Vapnik-Chervonenkis theory. The results follow from an analysis involving independent but possibly nonstationary training samples and can be extended, in a manner that we explain and illustrate, to relevant cases in which the training sample exhibits dependence.
