This article studies the convergence rate of the sample mean for $\varphi$-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.
翻译:本文章研究了以有限方式和无限差异混合成 美元 的 依赖性随机变量的样本平均值的趋同率。 将样本平均值分为主要部分的平均值和尾部部分的平均值,我们不仅获得了样本平均值的趋同率,而且还证明了主要部分平均值的趋同率比尾部部分平均值的趋同率要快。