Exponential inequalities for the distributions of canonical multiple partial sum processes
Teoriâ veroâtnostej i ee primeneniâ, Tome 64 (2019) no. 2, pp. 209-227 Cet article a éte moissonné depuis la source Math-Net.Ru

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Exponential inequalities are obtained for the distribution tail of the sup-norm of a multiple partial sum process with canonical bounded kernel based on independent and weakly dependent observations. The exponent obtained has the correct order.
Keywords: exponential inequalities, canonical $U$- and $V$-statistics, multiple orthogonal series.
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I. S. Borisov; A. A. Bystrov. Exponential inequalities for the distributions of canonical multiple partial sum processes. Teoriâ veroâtnostej i ee primeneniâ, Tome 64 (2019) no. 2, pp. 209-227. http://geodesic.mathdoc.fr/item/TVP_2019_64_2_a0/

[1] I. S. Borisov, V. A. Zhechev, “Invariance principle for canonical $U$- and $V$-statistics based on dependent observations”, Siberian Adv. Math., 25:1 (2015), 21–32 | DOI | MR | Zbl

[2] V. S. Korolyuk, Yu. V. Borovskikh, Theory of $U$-statistics, Math. Appl., 273, Kluwer Acad. Publ., Dordrecht, 1994, x+552 pp. | MR | MR | Zbl | Zbl

[3] W. Hoeffding, The strong law of large numbers for $U$-statistics, Inst. Statist. Mimeo Ser., Rep. No 302, North Carolina State Univ., 1961, 10 pp. http://www.lib.ncsu.edu/resolver/1840.4/2128

[4] W. Hoeffding, “Probability inequalities for sums of bounded random variables”, J. Amer. Statist. Assoc., 58:301 (1963), 13–30 | DOI | MR | Zbl

[5] I. S. Borisov, “Approximation of distributions of von Mises statistics with multidimensional kernels”, Siberian Math. J., 32:4 (1991), 554–566 | DOI | MR | Zbl

[6] M. A. Arcones, E. Gine, “Limit theorems for $U$-processes”, Ann. Probab., 21:3 (1993), 1494–1542 | DOI | MR | Zbl

[7] P. Major, “On a multivariate version of Bernstein's inequality”, Electron. J. Probab., 12 (2007), paper No 34, 966–988 | DOI | MR | Zbl

[8] P. S. Ruzankin, “Ob eksponentsialnykh neravenstvakh dlya kanonicheskikh $V$-statistik”, Sib. elektron. matem. izv., 11 (2014), 70–75 | MR | Zbl

[9] I. S. Borisov, N. V. Volodko, “Exponential inequalities for the distributions of canonical $U$- and $V$-statistics of dependent observations”, Siberian Adv. Math., 19:1 (2009), 1–12 | DOI | MR | Zbl

[10] I. S. Borisov, N. V. Volodko, “A note on exponential inequalities for the distribution tails of canonical von Mises' statistics of dependent observations”, Statist. Probab. Lett., 96 (2015), 287–291 | DOI | MR | Zbl

[11] A. N. Kolmogorov, S. V. Fomin, Elements of the theory of functions and functional analysis, v. I, II, Graylock Press, Albany, NY, 1957, 1961, ix+129 pp., ix+128 pp. | MR | MR | MR | Zbl | Zbl

[12] I. S. Borisov, N. V. Volodko, “Orthogonal series and limit theorems for canonical $U$- and $V$-statistics of stationary connected observations”, Siberian Adv. Math., 18:4 (2008), 242–257 | DOI | MR | Zbl

[13] A. A. Borovkov, “Notes on inequalities for sums of independent variables”, Theory Probab. Appl., 17:3 (1973), 556–557 | DOI | MR | Zbl

[14] J. L. Doob, Stochastic processes, John Wiley Sons, Inc., New York; Chapman Hall, Ltd., London, 1953, viii+654 pp. | MR | MR | Zbl

[15] J. Dedecker, C. Prieur, “New dependence coefficients. Examples and applications to statistics”, Probab. Theory Related Fields, 132:2 (2005), 203–236 | DOI | MR | Zbl

[16] Zhengyan Lin, Chuanrong Lu, Limit theory for mixing dependent random variables, Math. Appl., 378, Kluwer Acad. Publ., Dordrecht; Science Press Beijing, New York, 1996, xii+426 pp. | MR | Zbl