JSM 2004 - Toronto

Abstract #302079

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Activity Number: 54
Type: Contributed
Date/Time: Sunday, August 8, 2004 : 4:00 PM to 5:50 PM
Sponsor: General Methodology
Abstract - #302079
Title: Robust Fitting of Multinomial Models Based on Assessment of Model
Author(s): Jiawei Liu*+ and Bruce G. Lindsay
Companies: Pennsylvania State University and Pennsylvania State University
Address: 325 Thomas Bldg., Dept. of Statistics, University Park, PA, 16802,
Keywords: multinomial ; goodness of fit ; statistical tube ; model selection ; bootstrap ; semiparametric
Abstract:

We introduce a semiparametric tubular extension 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. Based on this idea one can define an index of fit of the model, to be the distance between the true multinomial distribution and the parametric model. 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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