Stein's method and poisson process convergence

Author:

Barbour A. D.

Abstract

Stein's method of obtaining rates of convergence, well known in normal and Poisson approximation, is considered here in the context of approximation by Poisson point processes, rather than their one-dimensional distributions. A general technique is sketched, whereby the basic ingredients necessary for the application of Stein's method may be derived, and this is applied to a simple problem in Poisson point process approximation.

Publisher

Cambridge University Press (CUP)

Subject

Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability

Reference11 articles.

1. On the rates in the central limit theorem for weakly dependent random fields

2. A bound for the error in the normal approximation to the distribution of a sum of dependent random variables;Stein;Proc. 6th Berkeley Symp. Math. Statist. Prob.,1970

3. Karr A. F. and Serfling R. J. (1987) Poisson approximation of Bernoulli point processes and their superpositions, via coupling.

4. Two central limit problems for dependent random variables

5. Poisson convergence and random graphs

Cited by 62 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Stein’s identities and the related topics: an instructive explanation on shrinkage, characterization, normal approximation and goodness-of-fit;Japanese Journal of Statistics and Data Science;2024-01-31

2. Analysis of Molecule Harvesting by Heterogeneous Receptors on MC Transmitters;2023 IEEE Globecom Workshops (GC Wkshps);2023-12-04

3. Normal approximation in total variation for statistics in geometric probability;Advances in Applied Probability;2023-07-03

4. A kernel Stein test for comparing latent variable models;Journal of the Royal Statistical Society Series B: Statistical Methodology;2023-05-06

5. Multivariate Stable Approximation by Stein’s Method;Journal of Theoretical Probability;2023-05-04

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3