Analysis of Divergence in Loglinear Models When Expected Frequencies are Subject to Linear Constraints |
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Authors: | Email author" target="_blank">L?PardoEmail author M?L?Menéndez |
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Institution: | (1) Department of Statistics and O.R., Facultad de Matemáticas, Plaza de Ciencias 3, Complutense University of Madrid, 28040 Madrid, Spain;(2) Department of Applied Mathematics, E.T.S.A.M., Polytechnical University of Madrid, Madrid, Spain |
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Abstract: | Consider the loglinear model for categorical data under the assumption of multinomial sampling. We are interested in testing between various hypotheses on the parameter space when we have some hypotheses relating to the parameters of the models that can be written in terms of constraints on the frequencies. The usual likelihood ratio test, with maximum likelihood estimator for the unspecified parameters, is generalized to tests based on -divergence statistics, using minimum -divergence estimator. These tests yield the classical likelihood ratio test as a special case. Asymptotic distributions for the new -divergence test statistics are derived under the null hypothesis. |
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Keywords: | Asymptotic distribution Multinomial sampling -divergence test statistics Loglinear models |
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