title: The central limit theorem under random truncation.
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 ∫ 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.
authors: Mathematical Institute, University of Giessen, Arndtstr. 2, D-35392 Giessen, Germany.  winfried.stute@math.uni-giessen.de.
authors: Winfried
authors: W
authors: Stute
authors: Jane-Ling
authors: JL
authors: Wang