Jonker, Marianne A.; van der Vaart, Aad W. A semi-parametric model for censored and passively registered data. (English) Zbl 0997.62077 Bernoulli 7, No. 1, 1-31 (2001). Summary: 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. Cited in 4 Documents MSC: 62N02 Estimation in survival analysis and censored data 62G20 Asymptotic properties of nonparametric inference 62N01 Censored data models 62G05 Nonparametric estimation 62F12 Asymptotic properties of parametric estimators Keywords:consistency; nuisance parameter; survival analysis; maximum likelihood; Grenander estimator PDFBibTeX XMLCite \textit{M. A. Jonker} and \textit{A. W. van der Vaart}, Bernoulli 7, No. 1, 1--31 (2001; Zbl 0997.62077) Full Text: DOI Euclid