A functional hungarian construction for sums of independent random variables
Annales de l'I.H.P. Probabilités et statistiques, Volume 38 (2002) no. 6, p. 923-957
@article{AIHPB_2002__38_6_923_0,
     author = {Grama, Ion and Nussbaum, Michael},
     title = {A functional hungarian construction for sums of independent random variables},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Elsevier},
     volume = {38},
     number = {6},
     year = {2002},
     pages = {923-957},
     zbl = {1021.60027},
     mrnumber = {1955345},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2002__38_6_923_0}
}
Grama, Ion; Nussbaum, Michael. A functional hungarian construction for sums of independent random variables. Annales de l'I.H.P. Probabilités et statistiques, Volume 38 (2002) no. 6, pp. 923-957. http://www.numdam.org/item/AIHPB_2002__38_6_923_0/

[1] J. Bretagnolle, P. Massart, Hungarian constructions from the nonasymptotic viewpoint, Ann. Probab. 17 (1989) 239-256. | MR 972783 | Zbl 0667.60042

[2] M. Csörgő, P. Révész, Strong Approximations in Probability and Statistics, Academic Press, New York, 1981. | MR 666546 | Zbl 0539.60029

[3] R. Dudley, Real Analysis and Probability, Wadsworth and Brooks/Cole, Pacific Grove, CA, 1989. | MR 982264 | Zbl 0686.60001

[4] U. Einmahl, Extensions on results of Komlós, Major and Tusnády to the multivariate case, J. Multivariate Anal. 28 (1989) 20-68. | MR 996984 | Zbl 0676.60038

[5] U. Einmahl, D.M. Mason, Gaussian approximation of local empirical processes indexed by functions, Probab. Theory Related Fields 107 (1997) 283-311. | MR 1440134 | Zbl 0878.60025

[6] I. Grama, M. Nussbaum, Asymptotic equivalence for nonparametric generalized linear models, Probab. Theory Related Fields 111 (1998) 167-214. | MR 1633574 | Zbl 0953.62039

[7] B.S. Kashin, A.A. Saakyan, Orthogonal Series, American Mathematical Society, Providence, RI, 1989. | MR 1007141 | Zbl 0668.42011

[8] V.I. Koltchinskii, Komlós-Major-Tusnády approximation for the general empirical process and Haar expansions of classes of functions, J. Theoret. Probab. 7 (1994) 73-118. | Zbl 0810.60002

[9] J. Komlós, P. Major, G. Tusnády, An approximation of partial sums of independent rv's and the sample df. I, Z. Wahrsch. verw. Gebiete 32 (1975) 111-131. | MR 375412 | Zbl 0308.60029

[10] J. Komlós, P. Major, G. Tusnády, An approximation of partial sums of independent rv's and the sample df. II, Z. Wahrsch. verw. Gebiete 34 (1976) 33-58. | MR 402883 | Zbl 0307.60045

[11] L. Le Cam, Asymptotic Methods in Statistical Decision Theory, Springer-Verlag, New York, 1986. | MR 856411 | Zbl 0605.62002

[12] L. Le Cam, G.L. Yang, Asymptotics in Statistics: Some Basic Concepts, Springer-Verlag, New York, 2000. | MR 1784901 | Zbl 0719.62003

[13] P. Massart, Strong approximation for multivariate empirical and related processes, via KMT constructions, Ann. Probab. 17 (1989) 266-291. | MR 972785 | Zbl 0675.60026

[14] M. Nussbaum, Asymptotic equivalence of density estimation and white noise, Preprint No. 35, Institute of Applied Analysis and Stochastics, Berlin, 1993. | MR 747259

[15] M. Nussbaum, Asymptotic equivalence of density estimation and Gaussian white noise, Ann. Statist. 24 (1996) 2399-2430. | MR 1425959 | Zbl 0867.62035

[16] E. Rio, Strong approximation for set-indexed partial sum processes, via K.M.T. constructions I, Ann. Probab. 21 (1993) 759-790. | MR 1217564 | Zbl 0776.60045

[17] E. Rio, Strong approximation for set-indexed partial sum processes, via K.M.T. constructions II, Ann. Probab. 21 (1993) 1706-1727. | MR 1235436 | Zbl 0779.60030

[18] E. Rio, Local invariance principles and their applications to density estimation, Probab. Theory Related Fields 98 (1994) 21-45. | MR 1254823 | Zbl 0794.60019

[19] A. Sakhanenko, The rate of convergence in the invariance principle for non-identically distributed variables with exponential moments, Limit theorems for sums of random variables. Trudy Inst. Matem., Sibirsk. Otdel. AN SSSR. 3 (1984) 3-49, (in Russian). | MR 749757 | Zbl 0541.60024

[20] A. Van Der Vaart, J. Wellner, Weak Convergence and Empirical Processes, Springer-Verlag, New York, 1996. | MR 1385671 | Zbl 0862.60002

[21] A. Zaitsev, On the Gaussian approximation of convolutions under multidimensional analogues of S.N. Bernstein's inequality conditions, Probab. Theory Related Fields 74 (1987) 534-566. | MR 876255 | Zbl 0612.60031

[22] A. Zaitsev, Estimates for quantiles of smooth conditional distributions and multidimensional invariance principle, Siberian Math. J. 37 (1996) 807-831. | MR 1643370 | Zbl 0881.60034

[23] A. Zaitsev, Multidimensional version of the results of Komlós, Major and Tusnády for vectors with finite exponential moments, ESAIM: P & S 2 (1998) 41-108. | Numdam | MR 1616527 | Zbl 0897.60033

[24] A. Zaitsev, Multidimensional version of a result of Sakhanenko in the invariance principle for vectors with finite exponential moments. I, Theory Probab. Appl. 45 (2001) 624-641. | MR 1968723 | Zbl 0994.60029