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Literature Cited
J. Komlos, P. Major, and G. Tusnady, “An approximation of partial sums of independent RV's and the sample DF,” Z. Wahrscheinlichkeitstheor. Verw. Geb.,32, No. 2, 111–131 (1975).
I. S. Borisov, “Rate of convergence in invariance principle in linear spaces. Application to empirical measures,” Lect. Notes Math.,1021, 45–58 (1983).
I. S. Borisov, “A new approach to the problem of approximating distributions of sums of independent random variables in linear spaces,” Trudy Mat. Inst., Sib. Sec., Academy of Sciences of the USSR,5, 3–27 (1985).
I. S. Borisov, “Rate of convergence in the invariance principle for empirical measures,” in: Proc. 1st World Congress Bernoulli Soc., VNU Sci. Press, Amsterdam (1987), pp. 833–836.
P. Massart, “Rates of convergence in the central limit theorem for empirical processes,” Ann. Inst. Henri Poincaré,22, 381–423 (1986).
P. Massart, “Strong approximation for multivariate empirical and related processes, via KMT constructions,” Ann. Probab.,17, 266–291 (1989).
V. I. Kolchinskii (Kolčinski), “Rates of convergence in the invariance principle for empirical processes,” Festschrift, Yu. Prokhorov et al. (eds.), VSP/Mokslas (1991).
E. Gine and J. Zinn, “Some limit theorems for empirical processes,” Ann. Probab.,12, 929–998 (1984).
V. N. Vapnik and A. Ya. Chervonenkis, “The uniform convergence of frequencies of the appearance of events to their probabilities,” Teor. Veroyatn. Primen.,16, 264–279 (1971).
V. N. Vapnik and A. Ya. Chervonenkis, “Necessary and sufficient condition of the uniform convergence of empirical means,” Teor. Veroyatn. Primen.,26, 543–563 (1981).
V. I. Kolchinskii, “The central limit theorem for empirical measures,” Teor. Veroyatn. Mat. Stat., Kiev,24, 63–75 (1981).
V. I. Kolchinskii, “Functional limit theorems and empirical entropy. I,” Teor. Veroyatn. Mat. Stat., Kiev,33, 35–45 (1985).
V. I. Kolchinskii, “Functional limit thoerems and empirical entropy. II,” Teor. Veroyatn. Mat. Stat., Kiev,34, 81–93 (1986).
L. Le Cam, “A remark on empirical processes,” in: Festschrift for E. L. Lehmann in Honor of His Sixty-Fifth Birthday, Belmont, California, Wadsworth (1983), pp. 305–327.
E. Gine and J. Zinn, “Lectures on the central limit theorem for empirical processes,” Lect. Notes Math.,1221, 50–113 (1986).
M. Talagrand, “Classes de Donsker et ensemble pulverisés,” C. R. Acad. Sci. Paris, Ser. I, 161–163 (1985).
R. M. Dudley, “Central limit theorems for empirical measures,” Ann. Probab.,6, 899–929 (1978).
A. N. Zhdanov and E. A. Sevast'yanov, “Approximative and differential properties of measurable sets,” Mat. Sb.,121, 403–422 (1983).
R. M. Dudley, “Metric entropy of some classes of sets with differentiable boundaries,” J. Approx. Theory,10, 227–236 (1974).
S. Csörgö, “Limit behaviour of the empirical characteristic function,” Ann. Probab.,9, 130–144 (1981).
M. B. Marcus and W. Philipp, “Almost sure invariance principles for sums of B-valued random variables with applications to random Fourier series and the empirical characteristic process,” Trans. Am. Math. Soc.,269, No. 1, 67–90 (1982).
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Kiev City. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 32, No. 4, pp. 48–60, July–August, 1991.
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Kolchinskii, V.I. Accuracy of the approximation of an empirical process by a Brownian bridge. Sib Math J 32, 578–588 (1991). https://doi.org/10.1007/BF00972976
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DOI: https://doi.org/10.1007/BF00972976