摘要翻译：
我们研究了一类广泛的基于核的回归(KBR)方法的统计性质。这些核方法是在过去十年中发展起来的，受到无限维Hilbert空间中凸风险最小化的启发。一个主要的例子是支持向量回归。我们首先描述了KBR方法的损失函数$L$与响应变量尾部之间的关系。然后，我们建立了KBR的$L$-风险一致性，这为这些方法能够“学习”的说法提供了数学证明。然后讨论了核方法的鲁棒性。特别地，我们的结果允许我们选择损失函数和核，以获得计算上易于处理和一致的具有有界影响函数的KBR方法。在此基础上，给出了影响函数的有限样本形式的偏置和灵敏度曲线的界，并讨论了KBR与经典M$估计之间的关系。
---
英文标题：
《Consistency and robustness of kernel-based regression in convex risk
  minimization》
---
作者：
Andreas Christmann, Ingo Steinwart
---
最新提交年份：
2007
---
分类信息：

一级分类：Mathematics        数学
二级分类：Statistics Theory        统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
--
一级分类：Statistics        统计学
二级分类：Statistics Theory        统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
--

---
英文摘要：
  We investigate statistical properties for a broad class of modern kernel-based regression (KBR) methods. These kernel methods were developed during the last decade and are inspired by convex risk minimization in infinite-dimensional Hilbert spaces. One leading example is support vector regression. We first describe the relationship between the loss function $L$ of the KBR method and the tail of the response variable. We then establish the $L$-risk consistency for KBR which gives the mathematical justification for the statement that these methods are able to ``learn''. Then we consider robustness properties of such kernel methods. In particular, our results allow us to choose the loss function and the kernel to obtain computationally tractable and consistent KBR methods that have bounded influence functions. Furthermore, bounds for the bias and for the sensitivity curve, which is a finite sample version of the influence function, are developed, and the relationship between KBR and classical $M$ estimators is discussed.
---
PDF链接：
https://arxiv.org/pdf/709.0626