A note on rates of convergence in the multidimensional CLT for maximum partial sums

Ibrahim A. Ahmad

Journal of Multivariate Analysis, 1979, vol. 9, issue 2, 314-321

Abstract: In this note we obtain rates of convergence in the central limit theorem for certain maximum of coordinate partial sums of independent identically distributed random vectors having positive mean vector and a nonsingular correlation matrix. The results obtained are in terms of rates of convergence in the multidimensional central limit theorem. Thus under the conditions of Sazonov (1968, Sankhya, Series A 30 181-204, Theorem 2), we have the same rate of convergence for the vector of coordinate maximums. Other conditions for the multidimensional CLT are also discussed, c.f., Bhattachaya (1977, Ann. Probability 5 1-27). As an application of one of the results we obtain a multivariate extension of a theorem of Rogozin (1966, Theor. Probability Appl. 11 438-441).

Keywords: Multidimensional; central; limit; theorem; maximum; partial; sums; independence; convergence; rates (search for similar items in EconPapers)
Date: 1979
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