arXiv subjects

N. Volodko

Publications and source records attributed to N. Volodko.

3 recordsLinked to original sources

arXiv2015

A note on exponential inequalities for the distribution tails of canonical von Mises' statistics of dependent observations

Hoeffding-type exponential inequalities are obtained for the distribution tails of canonical von Mises' statistics of arbitrary order based on samples from a stationary sequence of random variables satisfying the φ-mixing condition. The present paper weakens the restrictions on the coefficient φ() which are contained in the paper "Exponential inequalities for the distributions of canonical U- and V-statistics of dependent observations" by Borisov and Volodko (2009). At the same time, we correct the corresponding proof in this paper.

math.PR↗

arXiv2015

Exponential inequalities for the distribution tails of canonical U- and V-statistics of $ρ$-mixing observations

The Hoeffding-type-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 $ρ$-mixing.

math.PR↗

arXiv2009

Orthogonal series and limit theorems for canonical U- and V-statistics of stationary connected observations

The limit behavior is studied for the distributions of normalized U- and V-statistics of an arbitrary order with canonical (degenerate) kernels, based on samples of increasing sizes from a stationary sequence of observations satisfying classical mixing conditions. The corresponding limit distributions are represented as infinite multilinear forms of a centered Gaussian sequence with a known covariance matrix.

math.PR↗