Sharp orders of convergence in the random central limit theorem

DOI10.1016/0021-9045(88)90079-2zbMath0646.60024OpenAlexW1975258131MaRDI QIDQ1103946

Lothar Rogge, Dieter Landers

Publication date: 1988

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-9045(88)90079-2

zbMATH Keywords

Hausdorff distancerandom central limit theorem

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Rate of convergence, degree of approximation (41A25)

Related Items (4)

Random central limit theorem for associated random variables and the order of approximation ⋮ The exact approximation order of the random maximum Of cumulative sums Of independent variables ⋮ Convergence rates for stopped random sums ⋮ On the speed of convergence of the distribution of random sums of weighted independent variables

Cites Work

• General random sum limit theorems for martingales with large O-rates
• Almost sure equiconvergence of conditional expectations
• Some approximation methods for the distribution of random sums
• Uniform normal approximation orders for families of dominated measures
• Second-order approximation in the conditional central limit theorem
• An inequality for the Hausdorff-metric of \(\sigma\)-fields
• On the Berry-Esseen theorem for random U-statistics
• Uniform inequalities for conditional \(p\)-means given \(\sigma\)-lattices
• A counterexample in the approximation theory of random summation
• Uniform inequalities for conditional expectations
• Exact approximation orders in the conditional central limit theorem
• On the convergence rate of fixed-width sequential confidence intervals
• On the rate of convergence in the central limit theorem for Markov-chains
• The exact approximation order in the central-limit-theorem for random summation
• Equiconvergence of Martingales
• Note on the Tightness of the Metric on the Set of Complete Sub $\sigma$-Algebras of a Probability Space
• On the central limit theorem for the sum of a random number of independent random variables
• On the central limit theorem for the sum of a random number of independent random variables
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