论文标题
Stein在多元功能近似中的可交换对的方法
Stein's method of exchangeable pairs in multivariate functional approximations
论文作者
论文摘要
在本文中，我们通过合适的高斯工艺通过可交换对耦合来开发一个用于多元功能近似的框架，该耦合满足了合适的近似线性回归属性，从而在Barbour（1990）和Kasprzak（2020）的工作基础上建立了构建。我们一方面将结果应用于Erdős-renyi随机图模型中的联合子图计数以及对加权，退化$ u $ - 程序的矢量的适用性。作为后一类示例的具体实例，我们通过合适的高斯过程提供了多个长度的功能近似值的界限，即使在仅一次运行的情况下，它也将超出现有理论的范围。
In this paper we develop a framework for multivariate functional approximation by a suitable Gaussian process via an exchangeable pairs coupling that satisfies a suitable approximate linear regression property, thereby building on work by Barbour (1990) and Kasprzak (2020). We demonstrate the applicability of our results by applying it to joint subgraph counts in an Erdős-Renyi random graph model on the one hand and to vectors of weighted, degenerate $U$-processes on the other hand. As a concrete instance of the latter class of examples, we provide a bound for the functional approximation of a vector of success runs of different lengths by a suitable Gaussian process which, even in the situation of just a single run, would be outside the scope of the existing theory.
