The conditioned central limit theorem for the vector of maximum partial sums based on independent identically distributed random vectors is investigated and the rate of convergence is discussed. The conditioning is that of Rényi (1958,Acta Math. Acad. Sci. Hungar.,9, 215–228). Analogous results for the vector of partial sums are obtained.
AMS 1980 subject classification
Primary 60F05 Secondary 60G40, 60J15
Key words and phrases
Central limit theorem rates of convergence random vectors maximum sums
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