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Estimating a distribution function with truncated and censored data. (English) Zbl 0741.62037

Let \(X_ 1,X_ 2,\dots\) be i.i.d. random variables with a common distribution function \(F\). The problem of estimating \(F\) when \(X_ 1,X_ 2,\dots\) are subject to either trunction or censoring, or both, is considered. A modification of the Lynden-Bell-product-limit estimator is discussed and its asymptotic properties are established.

MSC:

62G05 Nonparametric estimation
62E20 Asymptotic distribution theory in statistics
62G20 Asymptotic properties of nonparametric inference
62F12 Asymptotic properties of parametric estimators
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