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Maximum likelihood estimation of a location parameter fails when the densityhave unbounded mode. An alternative approach is considered by leaving out adata point to avoid the unbounded density in the full likelihood. Thismodification give rise to the leave-one-out likelihood. We propose an ECMalgorithm which maximises the leave-one-out likelihood. It was shown that theestimator which maximises the leave-one-out likelihood is consistent andsuper-efficient. However, other asymptotic properties such as the optimal rateof convergence and asymptotic distribution is still under question. We usesimulations to investigate these asymptotic properties of the locationestimator using our proposed algorithm.

Maximum leave-one-out likelihood estimation for location parameter of unbounded densities