Discretized normal approximation by Stein's method

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 Erdös-Rényi random graph, and the uniform multinomial occupancy model.

Published in at http://dx.doi.org/10.3150/13-BEJ527 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)

References in corpus (3)

• Stein couplings for normal approximation
• Zero biasing and a discrete central limit theorem
• A Berry-Esseen bound for the uniform multinomial occupancy model

Cited by in corpus (8)

• Fixed point characterizations of continuous univariate probability distributions and their applications
• Non-integrable stable approximation by Stein's method
• Approximation of stable law in Wasserstein-1 distance by Stein's method
• Normal approximation in total variation for statistics in geometric probability
• Multivariate approximation in total variation, II: discrete normal approximation
• Error bounds in local limit theorems using Stein's method
• Local limit theorems for occupancy models
• Multivariate approximation in total variation, I: equilibrium distributions of Markov jump processes