摘要翻译:
本文考虑了一种新的bootstrap方法来估计高维$\ell_p$-统计量的分布,即[1,infty]$中的$n$独立的$d$-维随机向量之和的$\ell_p$-范数。本文给出了基于高斯近似的$\ell_p$-统计量抽样分布的非渐近刻画,并证明了bootstrap过程在Kolmogorov-Smirnov距离下在数据协方差结构温和的条件下是一致的。作为一般理论的应用,我们提出了一个bootstrap假设检验,用于高维均值向量的同时推理。我们在高维方案下建立了它的渐近正确性和一致性,并讨论了检验的幂以及相关置信度集的大小。我们在模拟数据上数值说明了引导和测试过程。
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英文标题:
《Bootstrapping $\ell_p$-Statistics in High Dimensions》
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作者:
Alexander Giessing, Jianqing Fan
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最新提交年份:
2020
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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:Economics 经济学
二级分类:Econometrics 计量经济学
分类描述:Econometric Theory, Micro-Econometrics, Macro-Econometrics, Empirical Content of Economic Relations discovered via New Methods, Methodological Aspects of the Application of Statistical Inference to Economic Data.
计量经济学理论,微观计量经济学,宏观计量经济学,通过新方法发现的经济关系的实证内容,统计推论应用于经济数据的方法论方面。
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一级分类:Mathematics 数学
二级分类:Probability 概率
分类描述:Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用:例如中心极限定理,大偏差,随机微分方程,统计力学模型,排队论
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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:
This paper considers a new bootstrap procedure to estimate the distribution of high-dimensional $\ell_p$-statistics, i.e. the $\ell_p$-norms of the sum of $n$ independent $d$-dimensional random vectors with $d \gg n$ and $p \in [1, \infty]$. We provide a non-asymptotic characterization of the sampling distribution of $\ell_p$-statistics based on Gaussian approximation and show that the bootstrap procedure is consistent in the Kolmogorov-Smirnov distance under mild conditions on the covariance structure of the data. As an application of the general theory we propose a bootstrap hypothesis test for simultaneous inference on high-dimensional mean vectors. We establish its asymptotic correctness and consistency under high-dimensional alternatives, and discuss the power of the test as well as the size of associated confidence sets. We illustrate the bootstrap and testing procedure numerically on simulated data.
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PDF链接:
https://arxiv.org/pdf/2006.13099