2008/08/01 by Winfried Stute, Jane-Ling Wang · 1 citation
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #Financial Risk and Volatility Modeling #Probability and Risk Models #Statistical Methods and Inference #math.ST #stat.TH
paper · pdf · doi:10.3150/07-bej116
published as Bernoulli 2008, Vol. 14, No. 3, 604-622 · Published in at http://dx.doi.org/10.3150/07-BEJ116 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)
openalex publication_date 2008/08/01 · arxiv created 2008/10/22 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/31
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.