Divergences and Duality for Estimation and Test under Moment Condition Models

Details Divergences and Duality for Estimation and Test under Moment Condition Models Divergences and Duality for Estimation and Test under Moment Condition Models

2010-02-03

arxiv.org/abs/1002.0730v3

Mathematics

Statistics Theory

37 pages, 4 figures

Scientific paper

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 misspeci?cation. 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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