Divergences and duality for estimation and test under moment condition models |
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Authors: | Michel Broniatowski Amor Keziou |
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Institution: | 1. LSTA, Université Pierre et Marie Curie, Paris 6, France;2. Laboratoire de Mathématiques de Reims, EA 4535, Université de Reims Champagne-Ardenne, France |
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Abstract: | We introduce estimation and test procedures through divergence minimization for models satisfying linear constraints with unknown parameter. These procedures extend the empirical likelihood (EL) method and share common features with generalized empirical likelihood approach. We treat the problems of existence and characterization of the divergence projections of probability distributions on sets of signed finite measures. We give a precise characterization of duality, for the proposed class of estimates and test statistics, which is used to derive their limiting distributions (including the EL estimate and the EL ratio statistic) both under the null hypotheses and under alternatives or misspecification. An approximation to the power function is deduced as well as the sample size which ensures a desired power for a given alternative. |
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Keywords: | Empirical likelihood Generalized empirical likelihood Minimum divergence Efficiency Power function Duality Divergence projection |
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