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It is well-known that in some situations it is not easy to compute thelikelihood function as the datasets might be large or the model is too complex.In that contexts composite likelihood, derived by multiplying the likelihoodsof subjects of the variables, may be useful. The extension of the classicallikelihood ratio test statistics to the framework of composite likelihoods isused as a procedure to solve the problem of testing in the context of compositelikelihood. In this paper we introduce and study a new family of teststatistics for composite likelihood: Composite {\phi}-divergence teststatistics for solving the problem of testing a simple null hypothesis or acomposite null hypothesis. To do that we introduce and study the asymptoticdistribution of the restricted maximum composite likelihood estimate.

On divergences tests for composite hypotheses under composite likelihood