I. S. Borisov, N. V. Volodko, “Exponential inequalities for the distributions of canonical $U$- and $V$-statistics of dependent observations”, Mat. Tr., 2008, Volume 11, Number 2,Pages 3

This article is cited in 11 papers

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

I. S. Borisov^ab, N. V. Volodko^ab

^a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
^b Novosibirsk State University

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 $\varphi$-mixing.

Key words: stationary sequence of random variables, $\varphi$-mixing, multiple orthogonal series, canonical $U$- and $V$-statistics.

UDC: 519.21

Received: 18.06.2008