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The central limit theorem under random truncation



The central limit theorem under random truncation



Bernoulli 14(3): 604-622



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 ∫ φ dF(n) of the nonparametric maximum likelihood estimator (MLE) of F, the Lynden-Bell estimator F(n). A useful representation of ∫ φ dF(n) 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.

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Accession: 056257478

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PMID: 22844204

DOI: 10.3150/07-BEJ116



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