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Survival analysis under cross-sectional sampling: length bias and multiplicative censoring. (English) Zbl 0969.62062
Summary: Consider a parametric, nonparametric or semiparametric model for survival times. Interest is in estimation of Euclidean and Banach parameters for these models. However, not the survival times themselves will be observed, since this might be quite time consuming. Instead, cross-sectional sampling is applied: at some point in time one identifies a random sample from the population under study and one registers the survival time up to this time-point. Typically, the resulting reduced survival times do not have the same distributions as the true survival times.
On the one hand, longer survival times have a higher probability to be sampled than smaller ones. On the other hand, the observed survival times have been censored multiplicatively. The length bias and multiplicative censoring properties of cross-sectional sampling will be discussed and reviewed as well as estimation in the resulting parametric, nonparametric, and semiparametric models.

##### MSC:
 62N02 Estimation in survival analysis and censored data 62G05 Nonparametric estimation 62F12 Asymptotic properties of parametric estimators 62G07 Density estimation 62G20 Asymptotic properties of nonparametric inference 46N30 Applications of functional analysis in probability theory and statistics 62M09 Non-Markovian processes: estimation
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