2020/09/13 by Aurélien Bibaut, Alex Luedtke, Bibaut, Aurélien F. +3
Economics, Econometrics and Finance · Mathematics · #Approximation Theory and Sequence Spaces #FOS: Mathematics #Iterative Methods for Nonlinear Equations #Statistics Theory (math.ST) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2009.05974
openalex publication_date 2020/09/13 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28
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.