LIKELIHOOD BASED INFERENCE FOR CURRENT STATUS DATA ON A GRID: A BOUNDARY PHENOMENON AND AN ADAPTIVE INFERENCE PROCEDURE

• 成果类型: Article
• 署名作者: Tang, Runlong; Banerjee, Moulinath; Kosorok, Michael R.
• 署名单位: Princeton University; University of Michigan System; University of Michigan; University of North Carolina; University of North Carolina Chapel Hill
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/11-AOS942
• 发表日期: 2012
• 页码: 45-72
• 关键词: interval-censored-data; estimators; bootstrap; discrete; density; times; MODEL; gmle

摘要

In this paper, we study the nonparametric maximum likelihood estimator for an event time distribution function at a point in the current status model with observation times supported on a grid of potentially unknown sparsity and with multiple subjects sharing the same observation time. This is of interest since observation time ties occur frequently with current status data. The grid resolution is specified as cn(-gamma) with c > 0 being a scaling constant and gamma > 0 regulating the sparsity of the grid relative to n, the number of subjects. The asymptotic behavior falls into three cases depending on gamma: regular Gaussian-type asymptotics obtain for gamma < 1/3, nonstandard cube-root asymptotics prevail when gamma > 1/3 and gamma = 1/3 serves as a boundary at which the transition happens. The limit distribution at the boundary is different from either of the previous cases and converges weakly to those obtained with gamma is an element of (0, 1/3) and gamma is an element of (1/3, infinity) as c goes to infinity and 0, respectively. This weak convergence allows us to develop an adaptive procedure to construct confidence intervals for the value of the event time distribution at a point of interest without needing to know or estimate gamma, which is of enormous advantage from the perspective of inference. A simulation study of the adaptive procedure is presented.