Bernoulli

  • Bernoulli
  • Volume 20, Number 3 (2014), 1404-1431.

Discretized normal approximation by Stein’s method

Xiao Fang

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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.

Article information

Source
Bernoulli, Volume 20, Number 3 (2014), 1404-1431.

Dates
First available in Project Euclid: 11 June 2014

Permanent link to this document
https://projecteuclid.org/euclid.bj/1402488944

Digital Object Identifier
doi:10.3150/13-BEJ527

Mathematical Reviews number (MathSciNet)
MR3217448

Zentralblatt MATH identifier
1310.62021

Keywords
discretized normal approximation exchangeable pairs local dependence size biasing Stein coupling Stein’s method

Citation

Fang, Xiao. Discretized normal approximation by Stein’s method. Bernoulli 20 (2014), no. 3, 1404--1431. doi:10.3150/13-BEJ527. https://projecteuclid.org/euclid.bj/1402488944


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References

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