Bernoulli

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

The central limit theorem under random truncation

Winfried Stute and Jane-Ling Wang

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Abstract

Under left truncation, data (Xi, Yi) are observed only when YiXi. Usually, the distribution function F of the Xi is the target of interest. In this paper, we study linear functionals ∫ϕ dFn of the nonparametric maximum likelihood estimator (MLE) of F, the Lynden-Bell estimator Fn. A useful representation of ∫ϕ dFn is derived which yields asymptotic normality under optimal moment conditions on the score function ϕ. 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
http://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. http://projecteuclid.org/euclid.bj/1219669622.


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