Rate of convergence in the central limit theorem for random variables with strong mixing

DOI10.1007/BF00970405zbMath0558.60023MaRDI QIDQ762831

Jonas Kazys Sunklodas

Publication date: 1984

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

zbMATH Keywords

convergence ratecentral limit theoremstrong mixing condition

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05)

Related Items (19)

Estimate of the rate of convergence in the central limit theorem for weakly dependent random fields ⋮ About estimation of ARIMA process with strong mixing MA part ⋮ Approximation of distributions of sums of weakly dependent random variables by the normal distribution ⋮ Improvement of the rate of convergence in the multidimensional central limit theorem for m-dependent random vectors ⋮ Oracally Efficient Two-Step Estimation of Generalized Additive Model ⋮ Canonical Trees, Compact Prefix-Free Codes, and Sums of Unit Fractions: A Probabilistic Analysis ⋮ On a lower bound of the rate of convergence in the central limit theorem for \(m\)-dependent random variables ⋮ Compound Poisson approximations for sums of 1-dependent random variables. I ⋮ From van der Corput to modern constructions of sequences for quasi-Monte Carlo rules ⋮ Polynomial spline confidence bands for time series trend ⋮ Convergence rates in the functional CLT for \(\alpha\)-mixing triangular arrays ⋮ Forward-selected panel data approach for program evaluation ⋮ Modelling time trend via spline confidence band ⋮ Central limit theorems for high dimensional dependent data ⋮ Kernel estimation of multivariate cumulative distribution function ⋮ Spline-backfitted kernel smoothing of partially linear additive model ⋮ Simultaneous confidence bands for time-series prediction function ⋮ Precise distribution properties of the van der Corput sequence and related sequences ⋮ Central limit theorem for finitely-dependent random variables

Cites Work

• \(L_\infty\)-bound for asymptotic normality of weakly dependent summands using Stein's result
• Moment inequalities for mixing sequences
• The central limit theorem for dependent random variables
• A CENTRAL LIMIT THEOREM AND A STRONG MIXING CONDITION
• On the speed of convergence in the random central limit theorem for ?-mixing processes
• Convergence rates of the strong law for stationary mixing sequences
• The Remainder in the Central Limit Theorem for Mixing Stochastic Processes
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