@article{PS_1998__2__41_0,
author = {Zaitsev, A. Yu.},
title = {Multidimensional version of the results of {Koml\'os,} {Major} and {Tusn\'ady} for vectors with finite exponential moments},
journal = {ESAIM: Probability and Statistics},
pages = {41--108},
publisher = {EDP-Sciences},
volume = {2},
year = {1998},
mrnumber = {1616527},
zbl = {0897.60033},
language = {en},
url = {http://archive.numdam.org/item/PS_1998__2__41_0/}
}
TY - JOUR AU - Zaitsev, A. Yu. TI - Multidimensional version of the results of Komlós, Major and Tusnády for vectors with finite exponential moments JO - ESAIM: Probability and Statistics PY - 1998 SP - 41 EP - 108 VL - 2 PB - EDP-Sciences UR - http://archive.numdam.org/item/PS_1998__2__41_0/ LA - en ID - PS_1998__2__41_0 ER -
%0 Journal Article %A Zaitsev, A. Yu. %T Multidimensional version of the results of Komlós, Major and Tusnády for vectors with finite exponential moments %J ESAIM: Probability and Statistics %D 1998 %P 41-108 %V 2 %I EDP-Sciences %U http://archive.numdam.org/item/PS_1998__2__41_0/ %G en %F PS_1998__2__41_0
Zaitsev, A. Yu. Multidimensional version of the results of Komlós, Major and Tusnády for vectors with finite exponential moments. ESAIM: Probability and Statistics, Tome 2 (1998), pp. 41-108. http://archive.numdam.org/item/PS_1998__2__41_0/
( 1966), Die Bestiminung der zu einem wiederkehrenden Prozess gehörenden Verteilungfunktion aus den mit Fehlern behafteten Daten einer einzigen Realisation, Studia Sci. Math. Hungar. 1 161-168. | MR | Zbl
( 1982), Fast sichere Approximation von Partialsummen unabhängiger und stationärer ergodischer Folgen von Zufallsveetoren, Dissertation, Universität Göttingen.
, ( 1979), Approximation theorems for independent and weakly dependent random vectors, Ann. Probab. 7 29-54. | MR | Zbl
( 1973), On the rate of convergence in the invariance principle, Theor. Probab. Appl. 18 207-225. | MR | Zbl
, ( 1975), A new method to prove Strassen type laws of invariance principle. I; II, Z. Wahrscheinlichkeitstheor. verw. Geb. 31 255-259; 261-269. | MR | Zbl
, ( 1981), Strong approximations in probability and statistics, Academic Press. | MR | Zbl
, ( 1984), The Komlós-Major-Tusnády approximations and their applications, Austral J. Statist. 26 189-218. | MR | Zbl
( 1953), Stochastic processes, Wiley. | MR | Zbl
( 1986), A refinement of the KMT-inequality for partial sumstrong approximation, Techn. Rep. Ser. Lab. Res. Statist. No. 88. Carleton University, University of Ottawa.
( 1987a), A useful estimate in the multidimensional invariance principle, Probab. Theor. Rel Fields 76 81-101. | MR | Zbl
( 1987b), Strong invariance principles for partial sums of independent random vectors, Ann. Probab. 15 1419-1440. | MR | Zbl
( 1989), Extensions of results of Komlós, Major and Tusnády to the multivariate case, J. Multivar. Anal. 28 20-68. | MR | Zbl
, ( 1997), Multidimensional Hungarian construction for almost Gaussian smooth distributions, Preprint 97- 071 SFB 343, Universität Bielefeld.
, , ( 1975; 1976), An approximation of partial sums of independent RV'-s and the sample DF. I; II, Z. Wahrscheinlichkeitstheor. verw. Geb. 32 111-131; 34 34-58. | MR | Zbl
( 1989), Strong approximation for multivariate empirical and related processes, via KMT construction, Ann. Probab. 17 266-291. | MR | Zbl
( 1979), Almost sure invariance principles for sums of B-valued random variables, Lect. Notes in Math. 709 171-193. | MR | Zbl
( 1956), Convergence of random processes and limit theorem of probability theory, Theor. Probab. Appl. 1 157-214. | MR | Zbl
( 1952), Remarks on a multivariate transformation, Ann. Math. Statist. 23 470-472. | MR | Zbl
( 1984), Rate of convergence in the invariance principles for variables with exponential moments that are not identically distributed, In: Trudy Inst. Mat. SO AN SSSR, Nauka, Novosibirsk, 3 4-49 (in Russian). | MR | Zbl
( 1981), Normal approximation - some recent advances, Lect. Notes in Math. 879. | MR | Zbl
( 1995), Strong approximation theorems for independent random variables and their applications, J. Multivar. Anal. 52 107-130. | MR | Zbl
( 1961), Studies in the theory of random processes, Univ. Kiev Press (in Russian, Engl. transl. ( 1965), Addison-Wesley). | MR | Zbl
( 1964), An invariance principle for the law of iterated logarithm, Z. Wahrscheinlichkeitstheor. verw. Geb. 3 211-226. | MR | Zbl
( 1978), On the error of the Gaussian approximation to the probability of a ball, Unpublished manuscript.
( 1986), Estimates of the Lévy-Prokhorov distance in the multivariate central limit theorem for random variables with finite exponential moments, Theor. Probab. Appl. 31 203-220. | MR | Zbl
( 1987), On the Gaussian approximation of convolutions under multi-dimensional analogues of S. N. Bernstein inequality conditions, Probab. Theor. Rel. Fields 74 535-566. | MR | Zbl
( 1988), On the connection between two classes of probability distributions, In: Rings and modulus. Limit theorems of probability theory. Vol. 2, Leningrad University Press, 153-158 (in Russian). | MR
( 1995a), Multidimensional version of the Hungarian construction, In : Vtoraya Vserossiiskaya shkola-kollokvium po stochasticheskim metodam. Ioshkar-Ola, 1995. Tezisy dokladov, TVP, Moskva, 54-55 (in Russian).
( 1995b), Multidimensional version of the results of Komlós, Major and Tusnády for vectors with finite exponential moments, Preprint 95 - 055 SFB 343, Universität Bielefeld.
( 1996a), An improvement of U. Einmahl estimate in the multidimensional invariance principle, In: Probability Theory and Mathematical Statistics. Proceedings of the Euler Institute Seminars Deducated to the Memory of Kolmogorov. I. A. Ibragimov and A. Yu. Zaitsev eds. Gordon and Breach, 109-116. | MR | Zbl
( 1996b), Estimates for quantiles of smooth conditional distributions and multidimensional invariance principle, Siberian Math. J. 37 807-831 (in Russian). | MR | Zbl
( 1997), Multidimensional variant of the Komlós, Major and Tusnády results for vectors with finite exponent ial moments, Dokl. Math. 56 935-937. | Zbl
