The Annals of Statistics

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

Winfried Stute

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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

Permanent link to this document
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
links.jstor.org

Subjects
Primary: 62G05: Estimation
Secondary: 62E20: Asymptotic distribution theory 62G30: Order statistics; empirical distribution functions

Keywords
Product-limit estimator truncated data almost sure representation

Citation

Stute, Winfried. Almost Sure Representations of the Product-Limit Estimator for Truncated Data. Ann. Statist. 21 (1993), no. 1, 146--156. doi:10.1214/aos/1176349019. http://projecteuclid.org/euclid.aos/1176349019.


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