论文标题
通过Stein操作员的扰动，本地依赖随机变量的总和近似
Approximation of Sums of Locally Dependent Random Variables via Perturbation of Stein Operator
论文作者
论文摘要
令$（x_ {i}，i \ in J）$为本地依赖的非负整数随机变量的家庭，并考虑sum $ w = \ sum \ sum \ nolimits_ {i \ in J} x_i $。我们首先使用Stein的方法为$ d_ {tv，m）$建立了一个通用错误上限，其中目标变量$ m $是泊松分布和二项式或负二项式分布的混合物。作为应用程序，我们达到$ o（| j |^{ - 1}）$ for（$ k_ {1}，k_ {2} $） - 运行和$ k $ -runs在某些特殊情况下。我们的结果是对文献中现有结果的显着改善，例如peköz[Bernoulli，19（2013）]和upadhye等人的$ O（1）$（1）$（1）$。 [Bernoulli，23（2017）]。
Let $(X_{i}, i\in J)$ be a family of locally dependent nonnegative integer-valued random variables, and consider the sum $W=\sum\nolimits_{i\in J}X_i$. We first establish a general error upper bound for $d_{TV}(W, M)$ using Stein's method, where the target variable $M$ is either the mixture of Poisson distribution and binomial or negative binomial distribution. As applications, we attain $O(|J|^{-1})$ error bounds for ($k_{1},k_{2}$)-runs and $k$-runs under some special cases. Our results are significant improvements of the existing results in literature, say $O(|J|^{-0.5})$ in Peköz [Bernoulli, 19 (2013)] and $O(1)$ in Upadhye, et al. [Bernoulli, 23 (2017)].
