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

TL;DR

This paper derives Hoeffding-type exponential inequalities for the distribution tails of canonical von Mises' statistics from dependent, stationary sequences, relaxing previous restrictions on the dependence measure and correcting earlier proofs.

Contribution

It extends exponential tail bounds to more general dependent data by weakening dependence restrictions and provides corrected proofs for these inequalities.

Findings

Established Hoeffding-type inequalities for dependent observations

Relaxed conditions on the {\varphi} dependence coefficient

Corrected previous proof errors in the literature

Abstract

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 {\varphi}-mixing condition. The present paper weakens the restrictions on the coefficient {\varphi}() 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.