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Title: Penalized minimum phi-divergence estimators in multinomial models Authors:  Virtudes Alba-Fernandez - University of Jaen (Spain) [presenting]
Maria Dolores Jimenez-Gamero - Universidad de Sevilla (Spain)
Abstract: The aim is to study the consequences of model misspecification for multinomial data when using penalized minimum Phi-divergence or penalized minimum disparity estimators to estimate the model parameters. These estimators are shown to converge to a well-defined limit. As an application of the results obtained, we consider the problem of testing goodness-of-fit to a given parametric family for multinomial data, using as test statistic a penalized divergence between the observed frequencies and a estimation of the null model cell probabilities. In some previous simulation studies, it has been observed that the asymptotic approximation to the null distribution of the test statistics in this class is rather poor. As an alternative way to approximate this null distribution, we prove that the bootstrap consistently estimates it. We present a numerical example illustrating the convenience of the bootstrap approximation which, in spite of demanding more computing time, it is more accurate than the approximation yielded by the asymptotic null distribution.