Parametric and semiparametric models for recapture and removal studies: a likelihood approach

Capture-recapture processes are biased samplings of recurrent event processes, which can be modelled by the Andersen-Gill intensity model. The intensity function is assumed to be a function of time, covariates and a parameter. We derive the maximum likelihood estimators of both the parameter and the population size and show the consistency and asymptotic normality of the estimators for both recapture and removal studies. The estimators are asymptotically efficient and their theoretical asymptotic relative efficiencies with respect to the existing estimators of Yip and co-workers can be as large as oc. The variance estimation and a numerical example are also presented.