On a lower bound of the rate of convergence in the central limit theorem for \(m\)-dependent random variables

DOI10.1007/BF02465362zbMath0897.60005OpenAlexW2910076083MaRDI QIDQ1386206

Jonas Kazys Sunklodas

Publication date: 14 May 1998

Published in: Lithuanian Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02465362

zbMATH Keywords

rate of convergencecentral limit theorem

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Limit theorems for vector-valued random variables (infinite-dimensional case) (60B12)

Related Items (1)

Compound Poisson approximations for sums of 1-dependent random variables. I

Cites Work

• Rate of convergence in the central limit theorem for random variables with strong mixing
• An Edgeworth expansion for a sum of m-dependent random variables
• Estimate of the rate of convergence in the central limit theorem for weakly dependent random fields
• Characterizing the rate of convergence in the central limit theorem
• On an L\(_p\) version of the Berry-Esseen theorem for independent and m- dependent variables
• \(L_1\) bounds for asymptotic normality of m-dependent sums using Stein's technique
• A central limit theorem for m-dependent random variables with unbounded m
• The central limit theorem for dependent random variables
• Reversing the Berry-Esseen Inequality
• Non-Uniform Estimates and Asymptotic Expansions of the Remainder in the Central Limit Theorem form-Dependent Random Variables
• LOWER BOUNDS FOR THE NORMAL APPROXIMATION OF A SUM OF INDEPENDENT RANDOM VARIABLES
• Non-Uniform Estimates, Moderate and Large Deviations in the Central Limit Theorem form-Dependent Random Variables
• On the Precision of an Estimate of the Remainder Term in the Central Limit Theorem
• On the Convergence Rate in the Central Limit Theorem for Weakly Dependent Random Variables
• A method for the derivation of limit theorems for sums of m-dependent random variables
• The Central Limit Theorem for Sums of Functions of Independent Variables and Sums of the Form $\sum {f(2^k t)} $
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