## The Annals of Statistics

### Almost Sure Representations of the Product-Limit Estimator for Truncated Data

Winfried Stute

#### Abstract

In the left-truncation model, one observes data $(X_i,Y_i)$ only when $Y_i\leq X_i$. Let F denote the marginal d.f. of $X_i$ , the variable of interest. The nonparametric MLE $\hat{F}_n$ of F aims at reconstructing F from truncated data. In this paper an almost sure representation of $\hat{F}_n$ is derived with improved error bounds on the one hand and under weaker distributional assumptions on the other hand.

#### Article information

Source
Ann. Statist. Volume 21, Number 1 (1993), 146-156.

Dates
First available in Project Euclid: 12 April 2007

http://projecteuclid.org/euclid.aos/1176349019

Digital Object Identifier
doi:10.1214/aos/1176349019

Mathematical Reviews number (MathSciNet)
MR1212170

Zentralblatt MATH identifier
0770.62027

JSTOR