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

TL;DR

This paper derives Hoeffding-type inequalities for the tail distributions of canonical U- and V-statistics based on stationary $ ho$-mixing sequences, providing probabilistic bounds for dependent data.

Contribution

It introduces new exponential tail inequalities for degenerate U- and V-statistics under $ ho$-mixing conditions, extending classical results to dependent observations.

Findings

Established Hoeffding-type inequalities for $ ho$-mixing sequences.

Provided bounds applicable to degenerate U- and V-statistics.

Extended tail probability estimates to dependent data contexts.

Abstract

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 $\rho$-mixing.