Berry-Esseen Bounds for Statistics of Non-Stationary, $\phi$-Mixing Random Variables

Abstract

Using a modification of Stein's method, we generalize the results of Bentkus, G{\"o}tze, and Tikhomirov \cite{bentkus1997berry} to obtain Berry-Esseen bounds for a broad class of statistics of sequences of $\phi$-mixing, non-stationary random variables with polynomial mixing rates. %and linear variance. We then consider applications of this theorem to ensure Berry-Esseen rates for various classes of non-stationary $\phi$-mixing random variables, including rates for a general class of processes of $\phi$-mixing random variables satisfying an aggregate third moment bound.