Asymptotic results for random sums of dependent random variables

DOI10.1016/j.spl.2015.10.015zbMath1382.60048OpenAlexW2096830998MaRDI QIDQ899626

Ümit Işlak

Publication date: 30 December 2015

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.spl.2015.10.015

zbMATH Keywords

random sumsStein's methodcentral limit theoremconcentration inequalitylocal dependence

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Sums of independent random variables; random walks (60G50)

Related Items (9)

Random central limit theorem for associated random variables and the order of approximation ⋮ On the rate of convergence in the global central limit theorem for random sums of uniformly strong mixing random variables ⋮ On some approximations for sums of \(m\)-dependent random variables ⋮ On the rates of convergence in central limit theorems for compound random sums of independent random variables ⋮ On the order of approximation in limit theorems for negative-binomial sums of strictly stationary \(m\)-dependent random variables ⋮ On the rate of convergence in the central limit theorem for random sums of strongly mixing random variables ⋮ AN EXTENSION OF RANDOM SUMMATIONS OF INDEPENDENT AND IDENTICALLY DISTRIBUTED RANDOM VARIABLES ⋮ On the rates of convergence in weak limit theorems for geometric random sums of the strictly stationary sequence of \(m\)-dependent random variables ⋮ Sum of a Random Number of Correlated Random Variables that Depend on the Number of Summands

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• A central limit theorem for \(m\)-dependent random variables
• Normal approximation under local dependence.
• Normal approximation for nonlinear statistics using a concentration inequality approach
• The central limit theorem for dependent random variables
• On adding a list of numbers (and other one-dependent determinantal processes)
• Normal Approximation by Stein’s Method
• A central limit theorem for randomly indexed m-dependent random variables
• Normal approximation for random sums
• The asymptotic distribution of the sum of a random number of random variables

This page was built for publication: Asymptotic results for random sums of dependent random variables