论文标题
订单统计的熵CLT
Entropic CLT for Order Statistics
论文作者
论文摘要
众所周知，随着样本量的增长，中央顺序统计数据表现出中心限制行为，并收敛到高斯分布。本文通过建立CLT的熵版本来增强这一已知结果，该版本可确保使用相对熵的更强的收敛方式。特别是，在轻度条件下，$ o（1/\ sqrt {n}）$收敛速率是基于生成订单统计数据的样本的父分布的。为了证明这一结果，得出了关于订单统计数据的辅助结果，这可能具有独立的利益。
It is well known that central order statistics exhibit a central limit behavior and converge to a Gaussian distribution as the sample size grows. This paper strengthens this known result by establishing an entropic version of the CLT that ensures a stronger mode of convergence using the relative entropy. In particular, an order $O(1/\sqrt{n})$ rate of convergence is established under mild conditions on the parent distribution of the sample generating the order statistics. To prove this result, ancillary results on order statistics are derived, which might be of independent interest.
