论文标题
自均衡的极限定理中的不均匀边界和Edgeworth扩展
Non-uniform bounds and Edgeworth expansions in self-normalized limit theorems
论文作者
论文摘要
我们研究了Edgeworth的扩展，以自称为单位的总和。建立了中心极限定理中扩展的不均匀边界，而仅施加最小的力矩条件。在此结果中，我们解决了非全力瞬间导致剩余减少的情况。此外，我们为局部极限定理的扩展提供了不均匀的边界。我们不均匀边界的增强尾巴准确性使得在熵中心限制定理中得出Edgeworth型扩展，以及在自分量总和的总变化距离中的中心极限定理。
We study Edgeworth expansions in limit theorems for self-normalized sums. Non-uniform bounds for expansions in the central limit theorem are established while only imposing minimal moment conditions. Within this result, we address the case of non-integer moments leading to a reduced remainder. Furthermore, we provide non-uniform bounds for expansions in local limit theorems. The enhanced tail-accuracy of our non-uniform bounds allows for deriving an Edgeworth-type expansion in the entropic central limit theorem as well as a central limit theorem in total variation distance for self-normalized sums.
