Abstract
In the paper, exponential inequalities are obtained for the distribution tail of the sup-norm of a V-process with canonical kernel based on independent or weakly dependent observations.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
I. S. Borisov, “Approximation of distributions of von Mises statistics with multidimensional kernels,” Sib. Mat. Zh. 32, 20 (1991). [Sib. Math. J. 32, 554 (1991)].
I. S. Borisov and N. V. Volod’ko, “Exponential inequalities for the distributions of canonical U- and V-statistics of dependent observations,” Mat. Tr. 11, 3 (2008) [Sib. Adv. Math., 19 1 (2009)].
I. S. Borisov and N. V. Volod’ko, “Orthogonal series and limit theorems for canonical U- and V-statistics of stationary observations,” Mat. Tr. 11, 25 (2008) [Sib. Adv. Math. 18, 242 (2008)].
I. S. Borisov and V. A. Zhechev, “Invariance principle for canonical U- and V-statistics based on dependent observations,” Mat. Tr. 16, 28 (2013) [Sib. Adv. Math. 25, 21 (2015)].
A. N. Kolmogorov and S. V. Fomin, Elements of the theory of functions and functional analysis. 3rd rev. ed. (Moscow, Nauka, 1972).
P. S. Ruzankin, “On exponential inequalities for canonical V-statistics,” Sib. Elektron. Mat. Izv. 11, 70 (2014).
I. S. Borisov and N. V. Volodko, “A note on exponential inequalities for the distribution tails of canonical Von Mises’ statistics of dependent observations,” Statist. Probab. Lett. 96, 287, 2015.
J. Dedecker and C. Prieur. “New dependence coefficients. Examples and applications to statistics,” Probab. Theory Relat. Fields 132, 203, 2005.
P. Doukhan, Mixing. Properties and Examples, Lecture Notes in Statist. 85 [New York, Springer-Verlag, 1994].
W. Hoeffding, “Probability inequalities for sums of bounded random variables,” J. Amer. Statist. Assoc. 18, 13 (1963).
Funding
The work of the first author was partially supported by the Russian Foundation for Basic Research (Project № 18-01-00074-a) and the Programme of Fundamental Scientific Research of SB RAS (Project № 0314-2016-0008).
Author information
Authors and Affiliations
Corresponding authors
Additional information
Russian Text © The Author(s), 2018, published in Matematicheskie Trudy, 2018, Vol. 21, No. 2, pp. 102–116.
About this article
Cite this article
Borisov, I.S., Zhechev, V.A. Exponential inequalities for the distributions of V-processes based on dependent observations. Sib. Adv. Math. 29, 263–273 (2019). https://doi.org/10.3103/S1055134419040023
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S1055134419040023