Summary
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.
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References
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Ahmad, I.A. Mixing normal approximations of vectors of sums and maximum sums. Ann Inst Stat Math 33, 375–383 (1981). https://doi.org/10.1007/BF02480948
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DOI: https://doi.org/10.1007/BF02480948