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Abstract: Using Implicit Function Theorem, we get the asymptotic expansion and normality of the minimum -divergence estimator which is seen to be a generalization of the maximum likelihood estimator for loglinear models under product-multinomial sampling. Then we use and -divergence measures to construct statistics in order to solve some classical problems including testing nested hypotheses. In last section we apply this method to a real data and do some simulation study to show the validness of and assess the finite-sample performance among different . [Copyright &y& Elsevier]

Abstract: Based on measures and minimum estimators , we present three families of test statistics for testing nonadditivity in loglinear models. The minimum estimator can be seen to be a generalization of the maximum likelihood estimator. In the process of testing nonadditivity, the two-stage tests procedure is usually used as the standard method. The unknown parameters are first estimated by some method (here ) and then these estimators which are treated as known constants are applied in the second-stage of this procedure. These three families of statistics which generalize the conclusions in Pardo and Pardo (2005) are asymptotically chi-squared. In the last section, we apply our method to a practical example and do a simulation study. [Copyright &y& Elsevier]