Discretized normal approximation by Stein's method

TL;DR

This paper develops a general theorem using Stein's method to bound the total variation distance between integer-valued distributions and discretized normal approximations, with applications to various probabilistic models.

Contribution

It introduces a new theorem for normal approximation of integer-valued variables and demonstrates its application to multiple complex probabilistic models.

Findings

Bound the total variation distance for specific models

Effective normal approximation for 2-runs in Bernoulli sequences

Application to Erdős-Rényi graph degrees and multinomial models

Abstract

We prove a general theorem to bound the total variation distance between the distribution of an integer valued random variable of interest and an appropriate discretized normal distribution. We apply the theorem to 2-runs in a sequence of i.i.d. Bernoulli random variables, the number of vertices with a given degree in the Erd\"{o}s-R\'{e}nyi random graph, and the uniform multinomial occupancy model.