MULTIVARIATE NORMAL APPROXIMATION WITH STEIN'SMETHOD OF EXCHANGEABLE PAIRS UNDER A GENERALLINEARITY CONDITION

GESINE REINERT; ADRIAN ROLLIN

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MULTIVARIATE NORMAL APPROXIMATION WITH STEIN'SMETHOD OF EXCHANGEABLE PAIRS UNDER A GENERALLINEARITY CONDITION

机译：一般线性条件下交换对的Stein'smethod的多元正态逼近

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In this paper we establish a multivariate exchangeable pairs approachwithin the framework of Stein's method to assess distributional distances topotentially singular multivariate normal distributions. By extending the statis-tics into a higher-dimensional space, we also propose an embedding methodwhich allows for a normal approximation even when the corresponding sta-tistics of interest do not lend themselves easily to Stein's exchangeable pairsapproach. To illustrate the method, we provide the examples of runs on theline as well as double-indexed permutation statistics.

机译：在本文中，我们在Stein方法的框架内建立了多元可交换对方法，以评估到潜在奇异多元正态分布的距离。通过将统计量扩展到更高维度的空间，我们还提出了一种嵌入方法，即使在相应的感兴趣的统计数据不容易适用于斯坦因的可交换对方法时，该方法也可以进行正态近似。为了说明该方法，我们提供了在线运行以及双索引排列统计的示例。

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《The Annals of Probability: An Official Journal of the Institute of Mathematical Statistics》 |2009年第6期|共24页
作者
GESINE REINERT; ADRIAN ROLLIN;
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原文格式 PDF
正文语种 eng
中图分类概率论（几率论、或然率论）;
关键词
APPROXIMATION; STEIN'S; CONDITION;

机译：近似;斯坦的;条件;

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专利

1. MULTIVARIATE NORMAL APPROXIMATION WITH STEIN'SMETHOD OF EXCHANGEABLE PAIRS UNDER A GENERALLINEARITY CONDITION [J] . GESINE REINERT, ADRIAN ROLLIN The Annals of Probability: An Official Journal of the Institute of Mathematical Statistics . 2009,第6期

机译：一般线性条件下交换对的Stein'smethod的多元正态逼近
2. Functional approximations via Stein's method of exchangeable pairs [J] . Kasprzak Mikolaj J. Annales de L'institut Henri Poincare . 2020,第4期

机译：通过Stein的可更换对方法的功能逼近
3. MULTIVARIATE NORMAL APPROXIMATIONS BY STEINS METHOD AND SIZE BIAS COUPLINGS [J] . Goldstein L., Rinott Y. Journal of Applied Probability . 1996,第1期

机译：用STEINS方法和尺寸偏置联轴器多变量正常近似
4. Face recognition based on geodesic distance approximations between multivariate normal distributions [C] . John Soldera, Kit Dodson, Jacob Scharcanski IEEE International Conference on Imaging Systems and Techniques . 2017

机译：基于多元正态分布之间测地距离近似的人脸识别
5. Exchangeable pairs in Stein's method of distributional approximation [D] . Ross, Nathan Forrest 2009

机译：Stein分布近似方法中的可交换对
6. EfficientImplementation of the Pair Atomic Resolutionof the Identity Approximation for Exact Exchange for Hybrid and Range-SeparatedDensity Functionals [O] . SamuelF. Manzer, Evgeny Epifanovsky, Martin Head-Gordon, -1

机译：高效的对原子分辨率的实现和距离分离的精确交换身份近似的估计密度功能
7. Multivariate normal approximation with Stein's method of exchangeable pairs under a general linearity condition [O] . Reinert, Gesine, Röllin, Adrian 2009

机译：用stein的可交换方法进行多元正态逼近一般线性条件下的对
8. Confidence Intervals for a Multivariate Normal Mean in the Case of Empirical Bayes Estimation Using Pearson Curves and Normal Approximations [R] . Vandermerwe, A. J., Groenewald, P. C. N., Nel, D. G., 1981

机译：利用pearson曲线和正态逼近进行经验Bayes估计的多元正态均值的置信区间

MULTIVARIATE NORMAL APPROXIMATION WITH STEIN'SMETHOD OF EXCHANGEABLE PAIRS UNDER A GENERALLINEARITY CONDITION

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