The central limit theorem under random truncation
| dc.creator | Stute, Winfried | |
| dc.creator | Wang, Jane-Ling | |
| dc.date | 2008-10-22 | |
| dc.date.accessioned | 2026-07-07T10:12:24Z | |
| dc.date.available | 2026-07-07T10:12:24Z | |
| dc.description | Under left truncation, data $(X_i,Y_i)$ are observed only when $Y_i\le X_i$. Usually, the distribution function $F$ of the $X_i$ is the target of interest. In this paper, we study linear functionals $\intφ\mathrm{d}F_n$ of the nonparametric maximum likelihood estimator (MLE) of $F$, the Lynden-Bell estimator $F_n$. A useful representation of $\int φ\mathrm{d}F_n$ 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. | |
| dc.description | 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) | |
| dc.identifier | https://arxiv.org/abs/0810.3985 | |
| dc.identifier | http://arxiv.org/abs/0810.3985 | |
| dc.identifier | Bernoulli 2008, Vol. 14, No. 3, 604-622 | |
| dc.identifier | doi:10.3150/07-BEJ116 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/172171 | |
| dc.subject | Statistics Theory | |
| dc.title | The central limit theorem under random truncation | |
| dc.type | text |