Title: Fast construction of efficient composite likelihood equations,
Abstract: 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 balancing
statistical efficiency and computing cost by minimizing an approximate distance
from the full likelihood score subject to a L1-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 properties are illustrated through
numerical examples.