Some simple variance bounds from Stein’s method

IF 0.6 4区 数学 Q4 STATISTICS & PROBABILITY
Fraser Daly, Fatemeh Ghaderinezhad, Christophe Ley, Yvik Swan
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引用次数: 0

Abstract

Using coupling techniques based on Stein’s method for probability approximation, we revisit classical variance bounding inequalities of Chernoff, Cacoullos, Chen and Klaassen. Our bounds are immediate in any context wherein a Stein identity is available. After providing illustrative examples for a Gaussian and a Gumbel target distribution, our main contributions are new variance bounds in settings where the underlying density function is unknown or intractable. Applications include bounds for analysis of the posterior in Bayesian statistics, bounds for asymptotically Gaussian random variables using zero-biased couplings, and bounds for random variables which are New Better (Worse) than Used in Expectation.
斯坦方法的一些简单方差限
利用基于Stein概率近似方法的耦合技术,我们回顾了Chernoff、Cacoullos、Chen和Klaassen的经典方差边界不等式。我们的界限在任何可以使用斯坦恒等式的情况下都是直接的。在提供了高斯和甘贝尔目标分布的说明性示例之后,我们的主要贡献是在潜在密度函数未知或难以处理的情况下设置新的方差界限。应用包括贝叶斯统计中后验分析的界,使用零偏耦合的渐近高斯随机变量的界,以及比期望中使用的新更好(更差)的随机变量的界。
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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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