Bernoulli

  • Bernoulli
  • Volume 14, Number 3 (2008), 604-622.

The central limit theorem under random truncation

Winfried Stute and Jane-Ling Wang

Full-text: Open access

Abstract

Under left truncation, data $(X_i, Y_i)$ are observed only when $Y_i≤X_i$. Usually, the distribution function $F$ of the $X_i$ is the target of interest. In this paper, we study linear functionals $∫\varphi \mathrm{d}F_n$ of the nonparametric maximum likelihood estimator (MLE) of $F$, the Lynden-Bell estimator $F_n$. A useful representation of $∫\varphi \mathrm{d}F_n$ is derived which yields asymptotic normality under optimal moment conditions on the score function $\varphi$. No continuity assumption on $F$ is required. As a by-product, we obtain the distributional convergence of the Lynden-Bell empirical process on the whole real line.

Article information

Source
Bernoulli, Volume 14, Number 3 (2008), 604-622.

Dates
First available in Project Euclid: 25 August 2008

Permanent link to this document
https://projecteuclid.org/euclid.bj/1219669622

Digital Object Identifier
doi:10.3150/07-BEJ116

Mathematical Reviews number (MathSciNet)
MR2537804

Zentralblatt MATH identifier
1157.62017

Keywords
central limit theorem Lynden-Bell integral truncated data

Citation

Stute, Winfried; Wang, Jane-Ling. The central limit theorem under random truncation. Bernoulli 14 (2008), no. 3, 604--622. doi:10.3150/07-BEJ116. https://projecteuclid.org/euclid.bj/1219669622


Export citation

References