Abstract #300763

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JSM 2002 Abstract #300763
Activity Number: 149
Type: Contributed
Date/Time: Monday, August 12, 2002 : 2:00 PM to 3:50 PM
Sponsor: IMS
Abstract - #300763
Title: The Tubular Extension of Multinomial Models
Author(s): Jiawei Liu*+ and Bruce Lindsay
Affiliation(s): Pennsylvania State University and Pennsylvania State University
Address: 325 Thomas Building, University Park, Pennsylvania, 16802, USA
Keywords: Multinomial ; Tubular Extension Model ; Statistical Distance ; Bootstrap
Abstract:

Let a given parametric model be specified for a multinomial distribution. We consider a nonparametric tubular extension which consists of all multinomial distributions in a neighborhood of the model. A probability vector can always be represented as an element of the tubular model, provided that the tube radius is large enough.

This paper defines a new index for evaluating goodness of fit of the parametric model, as the smallest tube radius required for the true multinomial parameter to be included into the extended model. We present methods for calculating the new index, making a statistical test, and constructing a lower confidence limit. A semi-parametric bootstrap method is used to simulate the distribution of the test statistics. A detailed discussion is given for the case in which the model is the row-column independence model and the statistical distance measure is Kullback-Leibler divergence.

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