发帖
雷达卡
摘要翻译：
本文给出了单位区间上非参数回归问题的统一方法。它是基于一个普遍的、诚实的、非渐近的置信域，该置信域由一组线性不等式定义，涉及设计点上的函数值。兴趣通常集中在该区域中某些最简单的函数上，其中简单性可以用形状（局部极值的数目、凸/凹的间隔）或光滑性（导数的界限）或两者的组合来定义。一旦确定了某种形式的正则化，置信域就可以用来提供诚实的非渐近置信界，这些置信界的信息量较少，但概念上要简单得多。
---
英文标题：
《Nonparametric Regression, Confidence Regions and Regularization》
---
作者：
P. L. Davies and A. Kovac and M. Meise
---
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：Methodology 方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
--
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：
In this paper we offer a unified approach to the problem of nonparametric regression on the unit interval. It is based on a universal, honest and non-asymptotic confidence region which is defined by a set of linear inequalities involving the values of the functions at the design points. Interest will typically centre on certain simplest functions in that region where simplicity can be defined in terms of shape (number of local extremes, intervals of convexity/concavity) or smoothness (bounds on derivatives) or a combination of both. Once some form of regularization has been decided upon the confidence region can be used to provide honest non-asymptotic confidence bounds which are less informative but conceptually much simpler.
---
PDF链接：
https://arxiv.org/pdf/711.069
京公网安备 11010802022788号
