Berry-Esseen bounds for self-normalized sums of locally dependent random variables

The Berry-Esseen bound provides an upper bound on the Kolmogorov distance between a random variable and the normal distribution. In this paper, we establish Berry-Esseen bounds with optimal rates for self-normalized sums of locally dependent random variables, assuming only a second-moment condition. Our proof leverages Stein’s method and introduces a novel randomized concentration inequality, which may also be of independent interest for other applications. Our main results have applied to self-normalized sums of m-dependent random variables and graph dependency models.