Geodesic
On accuracy of approximation in Koul’s theorem for weighted empirical processes
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 784-794.

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Using coupling we obtain an estimate for the distribution of the uniform distance between a given weighted empirical process and an accompanying gaussian process with the same mean and the covariance function. This estimate also allows us to obtain Koul’s theorem under more general sufficient assumptions.
Keywords: weighted empirical processes, gaussian approximation, accuracy of approximation, coupling, accompanying gaussian processes. 
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A. I. Sakhanenko; O. A. Sukhovershina. On accuracy of approximation in Koul’s theorem for weighted empirical processes. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 784-794. http://geodesic.mathdoc.fr/item/SEMR_2015_12_a37/

[1] H. L. Koul, Weighted Empirical Processes in Dynamic Nonlinear Models, Springer-Verlag, New York, 2002 | MR | Zbl

[2] I. I. Gikhman, A. V. Skorokhod, Vvedenie v teoriyu sluchainykh protsessov, Fizmatlit, M., 1965 | Zbl

[3] B. Marcus, J. Zinn, “The Bounded Law of the Iterated Logarithm for the Weighted Empirical Distribution Process in the Non-I.I.D. Case”, Annals of Probability, 12:2 (1984), 335–360 | DOI | MR | Zbl

[4] A. I. Sakhanenko, “A new way to obtain estimates in the invariance principle”, High Dimensional Probability II, eds. Gine et al., Birkhauser, Boston, 2000, 221–243 | MR

[5] A. V. Skorokhod, “Ob odnom predstavlenii sluchainykh velichin”, Teoriya veroyatnostei i ee primeneniya, 21:3 (1976), 645–648 | MR | Zbl