Bernstein inequality and moderate deviations under strong mixing conditions

TL;DR

This paper establishes a Bernstein inequality and moderate deviations principle for weakly dependent, bounded random variables with strong mixing conditions, extending existing large deviation results.

Contribution

It introduces a Bernstein inequality and moderate deviations principle for strongly mixing, bounded random variables, filling a gap in dependence-based probability inequalities.

Findings

Proves a Bernstein inequality for strongly mixing, bounded variables.

Derives a moderate deviations principle under exponential decay of mixing coefficients.

Complements previous large deviation results by Bryc and Dembo (1990s).

Abstract

In this paper we obtain a Bernstein type inequality for a class of weakly dependent and bounded random variables. The proofs lead to a moderate deviations principle for sums of bounded random variables with exponential decay of the strong mixing coeficients that complements the large deviation result obtained by Bryc and Dembo (1998) under superexponential mixing rates.