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Abstract
For a sequence of independent non-identically distributed random variables with positive means, rates of convergence of the maximum of their sums are established. These rates are exact and are obtained under the same moment conditions as those used for partial sums.
Keywords
Rates of convergence
maximum partial sums
central limit theorem
Article Details
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How to Cite
Ahmad, I. A., & Herawati, N. (2022). Convergence Rates of Maxima of Non-identical Sums. Pakistan Journal of Statistics and Operation Research, 18(1), 245-248. https://doi.org/10.18187/pjsor.v18i1.3746
References
- Ahmad, I.A. & Lin, P.E. (1977). A Berry-Essen type theorem. Utilitas Math., 11, 153-160
- Ahmad, I.A. (1979). A note on rates of convergence in the multidimensional CLT for maximum partial sums. J. Mult. Analysis, 9, 314-322
- Berry, A.C. (1941). The accuracy of the Gaussian approximation to the sum of independent variables. Trans. Amer. Math. Soc., 49, 122-136
- Esseen, C.G. (1945). Fourier analysis of distribution functions. A mathematical study of the Laplace-Gaussian Law. Acta. Math., 77, 1-125
- Katz, M. (1963). A note on the Berry-Esseen theorem. Ann. Math. Statist., 34, 1107-1108
- Friedman, N., Katz, M., & Koopmans, L.H. (1966). Convergence rates for the central limit theorem. Proc. Natl. Acad. Sci. USA., 56, 1062-1065
- Heyde, C.C. (1967). On the influence of moments on the rate of convergence to the normal distribution. Z. Wahrscheinlichkeitstheorie verw. Geb., 8, 12-18
- Petrov, V.V. (1965). An estimate of the deviation of the distribution of a sum of independent random variables from the normal law. Dokl. Akad. Nauk SSSR., 160, 1013-1015. (in Russian)
- Serova, G.V. (1979). On the rate of convergence in the central limit theorem. Theor. Prob. Math. Statist., 17, 121-130