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Exponential inequalities for the distributions of V-processes based on dependent observations

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.

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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).

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Corresponding authors

Correspondence to I. S. Borisov or V. A. Zhechev.

Additional information

Russian Text © The Author(s), 2018, published in Matematicheskie Trudy, 2018, Vol. 21, No. 2, pp. 102–116.

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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

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Keywords

  • exponential inequality
  • canonical U - and V -statistics
  • V -process
  • multiple orthogonal series
  • dependent observations
  • mixing conditions