  We introduce estimation and test procedures through divergence minimiza- tion
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 alterna- tives 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.
