Phi-Divergence Statistics for Testing Linear Hypotheses in Logistic Regression Models |
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Authors: | Maria Luisa Menéndez Julio Angel Pardo |
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Affiliation: | 1. Department of Applied Mathematics , ETSAM, Technical University of Madrid , Madrid, Spain;2. Department of Statistics and Operations Research I , Complutense University of Madrid , Madrid, Spain |
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Abstract: | In this paper we introduce and study two new families of statistics for the problem of testing linear combinations of the parameters in logistic regression models. These families are based on the phi-divergence measures. One of them includes the classical likelihood ratio statistic and the other the classical Pearson's statistic for this problem. It is interesting to note that the vector of unknown parameters, in the two new families of phi-divergence statistics considered in this paper, is estimated using the minimum phi-divergence estimator instead of the maximum likelihood estimator. Minimum phi-divergence estimators are a natural extension of the maximum likelihood estimator. |
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Keywords: | General linear hypotheses Logistic regression model Minimum phi-divergence estimator Phi-divergence statistic |
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