The Annals of Applied Probability

Stein's Method and Multinomial Approximation

Wei-Liem Loh

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Abstract

In this paper Stein's method is considered in the context of approximation by a multinomial distribution. By using a probabilistic argument of Barbour, whereby the essential ingredients necessary for the application of Stein's method are derived, the Stein equation for the multinomial distribution is obtained. Bounds on the smoothness of its solution are derived and are used in three examples to give error bounds for the multinomial approximation to the distribution of a random vector.

Article information

Source
Ann. Appl. Probab. Volume 2, Number 3 (1992), 536-554.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1177005648

Digital Object Identifier
doi:10.1214/aoap/1177005648

Mathematical Reviews number (MathSciNet)
MR1177898

Zentralblatt MATH identifier
0759.62007

JSTOR
links.jstor.org

Subjects
Primary: 60E15: Inequalities; stochastic orderings
Secondary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)

Keywords
Stein's method multinomial distribution rate of convergence multiurn Ehrenfest model total variation distance

Citation

Loh, Wei-Liem. Stein's Method and Multinomial Approximation. Ann. Appl. Probab. 2 (1992), no. 3, 536--554. doi:10.1214/aoap/1177005648. https://projecteuclid.org/euclid.aoap/1177005648


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