Consistency of the generalized MLE of a joint distribution function with multivariate interval-censored data |
| |
Authors: | Shaohua Yu Qiqing Yu George YC Wong |
| |
Institution: | a Novartis Pharmaceuticals Corporation, New Jersey, Binghamton University, New York, USA b Strang Cancer Prevention Center, New York, USA |
| |
Abstract: | Wong and Yu Generalized MLE of a joint distribution function with multivariate interval-censored data, J. Multivariate Anal. 69 (1999) 155-166] discussed generalized maximum likelihood estimation of the joint distribution function of a multivariate random vector whose coordinates are subject to interval censoring. They established uniform consistency of the generalized MLE (GMLE) of the distribution function under the assumption that the random vector is independent of the censoring vector and that both of the vector distributions are discrete. We relax these assumptions and establish consistency results of the GMLE under a multivariate mixed case interval censorship model. van der Vaart and Wellner Preservation theorems for Glivenko-Cantelli and uniform Glivenko-Cantelli class, in: E. Gine, D.M. Mason, J.A. Wellner (Eds.), High Dimensional Probability, vol. II, Birkhäuser, Boston, 2000, pp. 115-133] and Yu Consistency of the generalized MLE with multivariate mixed case interval-censored data, Ph.D Dissertation, Binghamton University, 2000] independently proved strong consistency of the GMLE in the L1(μ)-topology, where μ is a measure derived from the joint distribution of the censoring variables. We establish strong consistency of the GMLE in the topologies of weak convergence and pointwise convergence, and eventually uniform convergence under appropriate distributional assumptions and regularity conditions. |
| |
Keywords: | primary 62G20 secondary 62H12 |
本文献已被 ScienceDirect 等数据库收录! |
|