For inference in complex models, composite likelihood combines genuine likelihoods based on
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low-dimensional portions of the data, with weights to be chosen. Optimal weights in composite
likelihood may be searched following different routes, leading to a solution only in scalar
parametermodels. Here, after briefly reviewing themain approaches, we show how to obtain the
first-order optimal weights when using composite likelihood for inference on a scalar parameter
in the presence of nuisance parameters. These weights depend on the true parameter value and
need to be estimated. Under regularity conditions, the resulting likelihood ratio statistic has the
standard asymptotic null distribution and improved local power. Simulation results inmultivariate
normal models show that estimation of optimal weights maintains the standard approximate
null distribution and produces a visible gain in power with respect to constant weights.
