The exact approximation order of the random maximum Of cumulative sums Of independent variables

DOI10.1080/07474949308836274zbMath0771.62013OpenAlexW2062991747MaRDI QIDQ5286684

Stergios B. Fotopoulos

Publication date: 20 September 1993

Published in: Sequential Analysis (Search for Journal in Brave)

Full work available at URL: http://www.lib.ncsu.edu/resolver/1840.4/3640

zbMATH Keywords

rate of convergenceWiener processCUSUMBerry-Esseen inequalityquality controlstopping rulesindependent, identically distributed random variablesHausdorff-metricapproximation order of the uniform distancerandom maximum of cumulative sums

Mathematics Subject Classification ID

Asymptotic distribution theory in statistics (62E20) Sequential statistical methods (62L99)

Cites Work

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• Uniform normal approximation orders for families of dominated measures
• An inequality for the Hausdorff-metric of \(\sigma\)-fields
• Sharp orders of convergence in the random central limit theorem
• Convergence of some expected first passage times
• Exact approximation orders in the conditional central limit theorem
• Moment inequalities and the strong laws of large numbers
• A limit theorem for the maximum of cumulative sums
• On the Speed of Convergence of the Distribution of Maximum Sums of Independent Random Variables
• CONTINUOUS INSPECTION SCHEMES
• On certain limit theorems of the theory of probability
• 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