A NEW METHOD OF NORMAL APPROXIMATION
A NEW METHOD OF NORMAL APPROXIMATION
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DOI：
10.1214/07-aop370
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发表时间：
2006-11
影响因子：
2.3
通讯作者：
S. Chatterjee
中科院分区：
文献类型：
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作者：
S. Chatterjee
我们介绍了一个新版本的斯坦的方法，减少了一大类正常的逼近问题的方差界的练习，从而使中心极限定理和浓度之间的连接的措施。与Skorokhod嵌入不同，方差必须有界的对象有一个显式公式，可以更容易地执行程序。作为一个应用程序，我们得到了一个一般的CLT的功能，获得了许多当地的贡献，其中“当地”的定义本身取决于数据的组合。给出了几个例子，包括解决最近邻CLT问题所提出的P.Bickel。
We introduce a new version of Stein's method that reduces a large class of normal approximation problems to variance bounding exercises, thus making a connection between central limit theorems and concentration of measure. Unlike Skorokhod embeddings, the object whose variance must be bounded has an explicit formula that makes it possible to carry out the program more easily. As an application, we derive a general CLT for functions that are obtained as combinations of many local contributions, where the definition of "local" itself depends on the data. Several examples are given, including the solution to a nearest-neighbor CLT problem posed by P. Bickel.