  A maximum likelihood methodology for a general class of models is presented,
using an approximate Bayesian computation (ABC) approach. The typical target of
ABC methods are models with intractable likelihoods, and we combine an ABC-MCMC
sampler with so-called "data cloning" for maximum likelihood estimation.
Accuracy of ABC methods relies on the use of a small threshold value for
comparing simulations from the model and observed data. The proposed
methodology shows how to use large threshold values, while the number of
data-clones is increased to ease convergence towards an approximate maximum
likelihood estimate. We show how to exploit the methodology to reduce the
number of iterations of a standard ABC-MCMC algorithm and therefore reduce the
computational effort, while obtaining reasonable point estimates. Simulation
studies show the good performance of our approach on models with intractable
likelihoods such as g-and-k distributions, stochastic differential equations
and state-space models.
