Open Access
December 2009 Building and using semiparametric tolerance regions for parametric multinomial models
Jiawei Liu, Bruce G. Lindsay
Ann. Statist. 37(6A): 3644-3659 (December 2009). DOI: 10.1214/08-AOS603


We introduce a semiparametric “tubular neighborhood” of a parametric model in the multinomial setting. It consists of all multinomial distributions lying in a distance-based neighborhood of the parametric model of interest. Fitting such a tubular model allows one to use a parametric model while treating it as an approximation to the true distribution. In this paper, the Kullback–Leibler distance is used to build the tubular region. Based on this idea one can define the distance between the true multinomial distribution and the parametric model to be the index of fit. The paper develops a likelihood ratio test procedure for testing the magnitude of the index. A semiparametric bootstrap method is implemented to better approximate the distribution of the LRT statistic. The approximation permits more accurate construction of a lower confidence limit for the model fitting index.


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Jiawei Liu. Bruce G. Lindsay. "Building and using semiparametric tolerance regions for parametric multinomial models." Ann. Statist. 37 (6A) 3644 - 3659, December 2009.


Published: December 2009
First available in Project Euclid: 17 August 2009

zbMATH: 1369.62100
MathSciNet: MR2549573
Digital Object Identifier: 10.1214/08-AOS603

Primary: 62G35
Secondary: 62G15

Keywords: bootstrap , goodness of fit , Kullback–Leibler distance , Multinomial , tubular model

Rights: Copyright © 2009 Institute of Mathematical Statistics

Vol.37 • No. 6A • December 2009
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