论文标题
埃奇沃思（Edgeworth）扩展斯坦（Stein）的方法
Edgeworth Expansion by Stein's Method
论文作者
论文摘要
Edgeworth的扩展为概率分布的正常近似提供了更高的校正。 Edgeworth扩展的经典证明是通过特征功能。作为分布近似的强大方法，Stein的方法还被用于证明Edgeworth的扩展结果。但是，这些结果假定测试函数是平滑的（不包括半线的指示函数），或者随机变量是连续的（不包括只有连续组件的随机变量）。因此，如何使用Stein的方法恢复经典的Edgeworth扩展结果仍然是一个空旷的问题。在本文中，我们在一般情况下开发了Stein的两届Edgeworth扩展方法。我们的方法涉及反复使用Stein方程，通过Stein内核的Stein身份以及替代论点。
Edgeworth expansion provides higher-order corrections to the normal approximation for a probability distribution. The classical proof of Edgeworth expansion is via characteristic functions. As a powerful method for distributional approximations, Stein's method has also been used to prove Edgeworth expansion results. However, these results assume that either the test function is smooth (which excludes indicator functions of the half line) or that the random variables are continuous (which excludes random variables having only a continuous component). Thus, how to recover the classical Edgeworth expansion result using Stein's method has remained an open problem. In this paper, we develop Stein's method for two-term Edgeworth expansions in a general case. Our approach involves repeated use of Stein equations, Stein identities via Stein kernels, and a replacement argument.
