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Almost sure representations of the product-limit estimator for truncated data. (English) Zbl 0770.62027
Summary: In the left-truncation model, one observes data $(X\sb i,Y\sb i)$ only when $Y\sb i\le X\sb i$. Let $F$ denote the marginal d.f. of $X\sb i$, the variable of interest. The nonparametric MLE $\widehat F\sb n$ of $F$ aims at reconstructing $F$ from truncated data. An almost sure representation of $\widehat F\sb n$ is derived with improved error bounds on the one hand and under weaker distributional assumptions on the other hand.

62G05Nonparametric estimation
62G20Nonparametric asymptotic efficiency
62G30Order statistics; empirical distribution functions
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