AbstractWe study a selective sampling scheme in which survival data are observed during a data collection period if and only if a specific failure event is experienced. Individual units belong to one of a finite number of subpopulations, which may exhibit different survival behaviour, and thus cause heterogeneity. Based on a Poisson process model for individual emergence of population units, we derive a semiparametric likelihood model, in which the birth distribution is modeled nonparametrically and the lifetime distributions parametrically, and define maximum likelihood estimators. We propose a Newton–Raphson-type optimization method to address numerical challenges caused by the high-dimensional parameter space. The finite-sample properties and computational performance of the proposed algorithms are assessed in a simulation study. Personal insolvencies are studied as a special case of double truncation and we fit the semiparametric model to a medium-sized dataset to estimate the mean age at insolvency and the birth distribution of the underlying population.
An indirect proof for the asymptotic properties of VARMA model estimators