论文标题
CesàRO的随机收敛足够的条件不足
Sufficient and insufficient conditions for the stochastic convergence of Cesàro means
论文作者
论文摘要
我们研究了随机变量序列的cesàRO的随机收敛性。这些自然出现在具有顺序分量的统计问题中，其中随机变量的序列通常源自在数据上计算的一系列估计器。我们表明，确定序列的概率收敛速率通常不足以确定其均值的概率率。我们还对随机变量的顺序介绍了几组条件，这些条件足以保证其cesàRO平均值的收敛速率。我们确定了这些条件集合的共同设置。
We study the stochastic convergence of the Cesàro mean of a sequence of random variables. These arise naturally in statistical problems that have a sequential component, where the sequence of random variables is typically derived from a sequence of estimators computed on data. We show that establishing a rate of convergence in probability for a sequence is not sufficient in general to establish a rate in probability for its Cesàro mean. We also present several sets of conditions on the sequence of random variables that are sufficient to guarantee a rate of convergence for its Cesàro mean. We identify common settings in which these sets of conditions hold.
