Dipartimento di Scienze Statistiche

We focus on a capture-recapture model in which capture probabilities arise from an unspeci ed distri- bution F. We show that model parameters are identi able based on the unconditional likelihood. This is not true with the conditional likelihood. We also clarify that consistency and asymptotic equivalence of maximum likelihood estimators based on conditional and unconditional likelihood do not hold. We show that estimates of the undetected fraction of population based on the unconditional likelihood converge to the so-called estimable sharpest lower bound and we derive a new asymptotic equivalence result. We nally provide theoretical and simulation arguments in favour of the use of the unconditional likelihood rather than the conditional likelihood especially when one is willing to infer on the sharpest lower bound.