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Reliable inference for complex models by discriminative composite likelihood estimation

Composite likelihood estimation has an important role in the analysis of multivariate data for which the full likelihood function is intractable. An important issue in composite likelihood inference is the choice of the weights associated with lower-dimensional data sub-sets, since the presence of incompatible sub-models can deteriorate the accuracy of the resulting estimator. In this paper, we introduce a new approach for simultaneous parameter estimation by tilting, or re-weighting, each sub-likelihood component called discriminative composite likelihood estimation (D-McLE). The data-adaptive weights maximize the composite likelihood function, subject to moving a given distance from uniform weights; then, the resulting weights can be used to rank lower-dimensional likelihoods in terms of their influence in the composite likelihood function. Our analytical findings and numerical examples support the stability of the resulting estimator compared to estimators constructed using standard composition strategies based on uniform weights. The properties of the new method are illustrated through simulated data and real spatial data on multivariate precipitation extremes.