A semi-parametric model for censored and passively registered data

Abstract

We consider the estimation of the parameters in a semi-parametric model for life-history data from historical demography. The data consist of a sequence of times of life events that is either ended by a time of death or right-censored by an unobserved time of migration. We derive the properties of the maximum likelihood estimators of the parameters and prove their asymptotic efficiency. Estimating the migration distribution turns out to be an inverse problem, whereas the other parameters are regular. The proof is based on a uniform rate of convergence of the Grenander estimator of a monotone density and bounds on the number and spacings of its support points.