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References
Borisov I.S. Rate of convergence in central limit theorem for empirical measures.-Trans. of Math. Institute, Siberian Branch of the USSR Acad. of Sci. (in Russian), v. 3, to appear.
Borisov I.S. An approximation of empirical fields based on vector-valued observations with dependent coordinates.-Siberian Math. J. (in Russian), 1982, v.23, No 5, p.31–41.
Borovkov A.A. Remark about inequalities for sums of independent random variables.-Theory Prob. Appl. (in Russian), 1972, v.17, No 3, p.587–589.
Dudley R.M. Empirical processes, invariance principles and applications.-Third Vilnius Conf. on Prob. theory and math. statist., Abstracts of communic., Vilnius, 1981, v.3, p.72–75.
Fuk D.H., Nagaev S.V. Probability inequalities for sums of independent random variables.-Theory Probab. Appl. (in Russian), 1971, v.16, No 4, p.660–675.
Komlos J., Major P., Tusnady G. an approximation of partial sums of independent r.v.!s and sample DF.I.-Z. Wahrscheinlichkeitstheorie verw. Geb., 1975, B.32, No 1/2, S. 111–133.
Komlos J., Major P., Tusnady G. An approximation of partial sums of independent r.v!s and sample DF.II.-Z. Wahrscheinlichkeitstheorie verw. Geb., 1976, B.34, S. 33–58.
Major P. The approximation of partial sums of independent r.v!s.-Z. Wahrscheinlichkeitstheorie verw. Geb., 1976, B.35, No 3, S. 213–220.
Major P. Approximation of partial sums of i.i.d.r.v.'s when the summands have only two moments.-Z. Wahrscheinlichkeitstheorie verw. Geb., 1976, B.35, No 3, S. 221–229.
Philipp W., Pinzur L. Almost sure approximation theorems for the multivariate empirical process.-Z. Wahrscheinlichkeitstheorie verw. Geb., 1980, B.54, No 1, S. 1–13.
Sahanenko A.I. Estimates of the rate of convergence in the invariance principle.-Reports of the USSR Acad. Sci. (in Russian), 1974, v.219, No 5, p. 1076–1078.
Yurinskii V.V. Exponential inequalities for sums of random vectors.-J. Multivar. Anal., 1976, v.6, No 4, p.473–499.
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Borisov, I.S. (1983). Rate of convergence in invariance principle in linear spaces. Application to empirical measures. In: Prokhorov, J.V., Itô, K. (eds) Probability Theory and Mathematical Statistics. Lecture Notes in Mathematics, vol 1021. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072902
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DOI: https://doi.org/10.1007/BFb0072902
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