The central limit theorem under random truncation
Winfried Stute and Jane-Ling Wang
Source: Bernoulli
Volume 14, Number 3
(2008), 604-622.
Abstract
Under left truncation, data (Xi, Yi) are observed only when Yi≤Xi. 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.
Keywords: central limit theorem; Lynden-Bell integral; truncated data
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.bj/1219669622
Digital Object Identifier: doi:10.3150/07-BEJ116
Zentralblatt MATH identifier:
1157.62017
Mathematical Reviews number (MathSciNet):
MR2537804
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