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摘要翻译：
研究了具有未知依赖结构的随机向量均值的广义bootstrap置信域。随机向量要么是高斯分布，要么是对称有界分布。向量的维数可能比观测次数大得多，根据学习理论的最新结果，我们将重点放在置信度的非渐近控制上。我们考虑了两种方法，第一种基于集中原理（对一大类重采样权值有效），第二种基于重采样分位数，特别是使用Rademacher权值。在基于集中原则的方法中建立的几个中间结果本身是有意义的。我们还讨论了重采样量的蒙特卡罗近似的精度问题。
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英文标题：
《Some nonasymptotic results on resampling in high dimension, I:
Confidence regions, II: Multiple tests》
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作者：
Sylvain Arlot, Gilles Blanchard, Etienne Roquain
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最新提交年份：
2010
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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
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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。
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英文摘要：
We study generalized bootstrap confidence regions for the mean of a random vector whose coordinates have an unknown dependency structure. The random vector is supposed to be either Gaussian or to have a symmetric and bounded distribution. The dimensionality of the vector can possibly be much larger than the number of observations and we focus on a nonasymptotic control of the confidence level, following ideas inspired by recent results in learning theory. We consider two approaches, the first based on a concentration principle (valid for a large class of resampling weights) and the second on a resampled quantile, specifically using Rademacher weights. Several intermediate results established in the approach based on concentration principles are of interest in their own right. We also discuss the question of accuracy when using Monte Carlo approximations of the resampled quantities.
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PDF链接：
https://arxiv.org/pdf/712.0775
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