Normal approximation via non-linear exchangeable pairs

IF 0.6 4区 数学 Q4 STATISTICS & PROBABILITY
C. Dobler
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引用次数: 6

Abstract

We propose a new functional analytic approach to Stein's method of exchangeable pairs that does not require the pair at hand to satisfy any approximate linear regression property. We make use of this theory in order to derive abstract bounds on the normal and Gamma approximation of certain functionals in the Wasserstein distance. Moreover, we illustrate the relevance of this approach by means of three instances of situations to which it can be applied: Functionals of independent random variables, finite population statistics and functionals on finite groups. In the independent case, and in particular for symmetric $U$-statistics, we demonstrate in which respect this approach yields fundamentally better bounds than those in the existing literature. Finally, we apply our results to provide Wasserstein bounds in a CLT for subgraph counts in geometric random graphs based on $n$ i.i.d. points in Euclidean space as well as to the normal approximation of Pearson's statistic.
通过非线性交换对的正态逼近
我们提出了一种新的泛函解析方法的Stein的交换对的方法,它不要求手头的对满足任何近似线性回归性质。我们利用这一理论来推导某些泛函在Wasserstein距离上的正态近似和伽玛近似的抽象界。此外,我们通过可以应用这种方法的三个情况实例来说明这种方法的相关性:独立随机变量的泛函,有限总体统计和有限群上的泛函。在独立的情况下,特别是对于对称的$U$统计,我们证明了这种方法在哪些方面产生了比现有文献中更好的边界。最后,我们将我们的结果应用于基于欧几里德空间中n个点的几何随机图的子图计数的CLT中的Wasserstein边界以及Pearson统计量的正态近似。
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来源期刊
CiteScore
1.10
自引率
0.00%
发文量
48
期刊介绍: ALEA publishes research articles in probability theory, stochastic processes, mathematical statistics, and their applications. It publishes also review articles of subjects which developed considerably in recent years. All articles submitted go through a rigorous refereeing process by peers and are published immediately after accepted. ALEA is an electronic journal of the Latin-american probability and statistical community which provides open access to all of its content and uses only free programs. Authors are allowed to deposit their published article into their institutional repository, freely and with no embargo, as long as they acknowledge the source of the paper. ALEA is affiliated with the Institute of Mathematical Statistics.
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