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Berry, A.C.: The accuracy of the Gaussian approximation to the sum of independent variates. Trans. Amer. Math. Soc. 40, 122–136 (1941)
Cramér, H.: On the composition of elementary errors. Scand. Aktuar. 11, 13–74, 141–180 (1928)
Cramér, H.: Random variables and probability distributions. Cambridge Tracts in Mathematics No. 36, Cambridge: Cambridge University Press 1937
Esséen, C.-G.: Fourier analysis of distribution functions. A mathematical study of the Laplace-Gaussian law. Acta Math. 77, 1–125 (1945)
Gnedenko, B.V., Kolmogorov, A.N.: Limit Distributions for Sums of Independent Random Variables. Reading, Mass: Addison-Wesley 1954
Hall, P.: Characterising the rate of convergence in the central limit theorem. Ann. Probability 8, 1037–1048 (1980)
Hall, P.: Characterising the rate of convergence in the central limit theorem II. Math. Proc. Cambridge Philos. Soc. 89, 511–523 (1981)
Hall, P.: Rates of Convergence in the Central Limit Theorem. To appear Pitman's Research Notes in Mathematics
Heyde, C.C.: On the influence of moments on the rate of convergence to the normal distribution. Z. Wahrscheinlichkeitstheorie verw. Geb. 8, 12–18 (1967)
Heyde, C.C.: Some properties of metrics in a study of convergence to normality. Z. Wahrscheinlichkeitstheorie verw. Geb. 11, 181–192 (1969)
Heyde, C.C.: On the implication of a certain rate of convergence to normality. Z. Wahrscheinlichkeitstheorie verw. Geb. 16, 151–156 (1970)
Heyde, C.C., Leslie, J.R.: On the influence of moments on approximations by portion of a Chebyshev series in central limit convergence. Z. Wahrscheinlichkeitstheorie verw. Geb. 21, 255–268 (1972)
Höglund, Th.: On the convergence of convolutions of distributions with regularly varying tails. Z. Wahrscheinlichkeitstheorie verw. Geb. 15, 263–272 (1970)
Ibragimov, I.A.: On the accuracy of the Gaussian approximation to the distribution functions of sums of independent variables. Theor. Probability Appl. 11, 559–579 (1966)
Ibragimov, I.A.: On the Chebyshev-Cramér asymptotic expansions. Theor. Probability Appl. 12, 455–470 (1967)
Ibragimov, I.A., Linnik, Yu.V.: Independent and Stationary Sequences of Random Variables. Gröningen: Wolters-Noordhoff 1971
Leslie, J.R.: Generalisation and application of some results of Ibragimov on convergence to normality. Ann. Probability 3, 897–902 (1975)
Lifshitz, B.A.: On the accuracy of approximation in the central limit theorem. Theor. Probability Appl. 21, 108–124 (1976)
Maejima, M.: Some L p versions for the central limit theorem. Ann. Probability 6, 341–344 (1978)
Osipov, L.V.: On the closeness with which the distribution of the sum of independent random variables approximates the normal distribution. Soviet Math. Doklady 9, 233–236 (1968)
Osipov, L.V.: On asymptotic expansions for the distributions of sums of independent random variables. Theor. Probability Appl. 16, 333–343 (1971)
Petrov, V.V.: Sums of Independent Random Variables. Berlin-Heidelberg-New York: Springer 1975
Rozovskii, L.V.: On the precision of an estimate of the remainder term in the central limit theorem. Theor. Probability Appl. 23, 712–730 (1978)
Rozovskii, L.V.: On an estimate from below of the remainder term in the central limit theorem. Mat. Zametki 24, 411–418 (1978)
Seneta, E.: Regularly Varying Functions. Berlin-Heidelberg-New York: Springer 1976
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Hall, P. Fast rates of convergence in the central limit theorem. Z. Wahrscheinlichkeitstheorie verw Gebiete 62, 491–507 (1983). https://doi.org/10.1007/BF00534201
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DOI: https://doi.org/10.1007/BF00534201