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August, 1992 Stein's Method and Multinomial Approximation
Wei-Liem Loh
Ann. Appl. Probab. 2(3): 536-554 (August, 1992). DOI: 10.1214/aoap/1177005648


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.


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Wei-Liem Loh. "Stein's Method and Multinomial Approximation." Ann. Appl. Probab. 2 (3) 536 - 554, August, 1992.


Published: August, 1992
First available in Project Euclid: 19 April 2007

zbMATH: 0759.62007
MathSciNet: MR1177898
Digital Object Identifier: 10.1214/aoap/1177005648

Primary: 60E15
Secondary: 60J10

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

Rights: Copyright © 1992 Institute of Mathematical Statistics

Vol.2 • No. 3 • August, 1992
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