  Maximum likelihood estimation of a location parameter fails when the density
have unbounded mode. An alternative approach is considered by leaving out a
data point to avoid the unbounded density in the full likelihood. This
modification give rise to the leave-one-out likelihood. We propose an ECM
algorithm which maximises the leave-one-out likelihood. It was shown that the
estimator which maximises the leave-one-out likelihood is consistent and
super-efficient. However, other asymptotic properties such as the optimal rate
of convergence and asymptotic distribution is still under question. We use
simulations to investigate these asymptotic properties of the location
estimator using our proposed algorithm.
