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We introduce estimation and test procedures through divergence minimiza- tionfor models satisfying linear constraints with unknown parameter. Theseprocedures extend the empirical likelihood (EL) method and share commonfeatures with generalized empirical likelihood approach. We treat the problemsof existence and characterization of the divergence projections of probabilitydistributions on sets of signed finite measures. We give a precisecharacterization of duality, for the proposed class of estimates and teststatistics, which is used to derive their limiting distributions (including theEL estimate and the EL ratio statistic) both under the null hypotheses andunder alterna- tives or misspecification. An approximation to the powerfunction is deduced as well as the sample size which ensures a desired powerfor a given alternative.

Divergences and Duality for Estimation and Test under Moment Condition Models