Refined Exponential Inequalities for Acceptable Random Variables

Abstract

This paper establishes refined exponential inequalities for a wide class of acceptable random variables using a flexible exponential bound from the extended negative dependence framework. New moment bounds and concentration inequalities are derived, where a parameter replaces the classical variance with an absolute moment of a certain order. The corresponding convergence rate for the strong law of large numbers is obtained. The results unify and extend existing bounds for various dependent structures, including widely, extended negatively, negatively, and independent sequences. Applications to autoregressive models and nonparametric regression illustrate the practical utility of the theoretical findings.