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A semi-parametric model for censored and passively registered data. (English) Zbl 0997.62077

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.

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
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