Fast construction of efficient composite likelihood equations
Growth in both size and complexity of modern data challenges the applicability of traditional likelihood-based inference. Composite likelihood (CL) methods address the diﬃculties related to model selection and computational intractability of the full likelihood by combining a number of low-dimensional likelihood objects into a single objective function used for inference. This paper introduces a procedure to combine partial likelihood objects from a large set of feasible candidates and simultaneously carry out parameter estimation. The new method constructs estimating equations bal-ancing statistical eﬃciency and computing cost by minimizing an approximate distance from the full likelihood score subject to a 1-norm penalty representing the available computing resources. This results in truncated CL equations containing only the most informative partial likelihood score terms. An asymptotic theory within a framework where both sample size and data dimension grow is developed and ﬁnite-sample prop-erties are illustrated through numerical examples.