Building and using semiparametric tolerance regions for parametric multinomial models - Mathematics > Statistics TheoryReport as inadecuate




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Abstract: We introduce a semiparametric ``tubular neighborhood- of a parametric modelin the multinomial setting. It consists of all multinomial distributions lyingin a distance-based neighborhood of the parametric model of interest. Fittingsuch a tubular model allows one to use a parametric model while treating it asan approximation to the true distribution. In this paper, the Kullback-Leiblerdistance is used to build the tubular region. Based on this idea one can definethe distance between the true multinomial distribution and the parametric modelto be the index of fit. The paper develops a likelihood ratio test procedurefor testing the magnitude of the index. A semiparametric bootstrap method isimplemented to better approximate the distribution of the LRT statistic. Theapproximation permits more accurate construction of a lower confidence limitfor the model fitting index.



Author: Jiawei Liu, Bruce G. Lindsay

Source: https://arxiv.org/



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