具有厚尾分布的φ混合相依随机变量样本均值的收敛速度

Convergence Rate of Sample Mean forφ-Mixing Random Variables with Heavy-Tailed Distributions

本文研究了φ混合相依随机变量在有限均值和无穷方差下样本均值的收敛速度.将样本均值分解为主部均值和尾部均值之和,我们不仅得到了样本均值的收敛速度,而且证明了主部均值的收敛速度快于尾部均值的收敛速度.

This article studies the convergence rate of the sample mean forφ-mixing dependent random variables with finite means and infinite variances.Dividing the sample mean into sum of the average of the main parts and the average of the tailed parts,we not only obtain the convergence rate of the sample mean but also prove that the convergence rate of the average of the main parts is faster than that of the average of the tailed parts.