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Exponential inequalities for the distributions of canonical U- and V-statistics of dependent observations

Abstract

Exponential inequalities are obtained for the distribution tails of canonical (degenerate) U- and V-statistics of an arbitrary order based on samples from a stationary sequence of observations satisfying ϕ-mixing.

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Correspondence to I. S. Borisov.

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Original Russian Text © I. S. Borisov and N. V. Volodko, 2008, published in Matematicheskie Trudy, 2008, Vol. 11, No. 2, pp. 3–19.

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Borisov, I.S., Volodko, N.V. Exponential inequalities for the distributions of canonical U- and V-statistics of dependent observations. Sib. Adv. Math. 19, 1–12 (2009). https://doi.org/10.3103/S1055134409010015

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Key words

  • stationary sequence of random variables
  • φ-mixing
  • multiple orthogonal series
  • canonical U- and V-statistics