DeepAI
Log In Sign Up

Sufficient and insufficient conditions for the stochastic convergence of Cesàro means

09/13/2020
by   Aurélien F. Bibaut, et al.
0

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.

READ FULL TEXT

page 1

page 2

page 3

page 4

12/08/2018

Generalization of the pairwise stochastic precedence order to the sequence of random variables

We discuss a new stochastic ordering for the sequence of independent ran...
07/20/2022

Properties of complex-valued power means of random variables and their applications

We consider power means of independent and identically distributed (i.i....
09/18/2022

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

This article studies the convergence rate of the sample mean for φ-mixin...
10/19/2016

Consistent Kernel Mean Estimation for Functions of Random Variables

We provide a theoretical foundation for non-parametric estimation of fun...
08/29/2019

The network uncertainty quantification method for propagating uncertainties in component-based systems

This work introduces the network uncertainty quantification (NetUQ) meth...
11/24/2021

Lossy Compression of General Random Variables

This paper is concerned with the lossy compression of general random var...