Asymptotic theory for nonparametric estimation of survival curves under order restrictions

• 成果类型: Article
• 署名作者: Praestgaard, JT; Huang, J
• 署名单位: University of Iowa
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1996
• 页码: 1679-1716
• 关键词: Empirical Processes; LIMIT-THEOREMS

摘要

We consider two problems in nonparametric survival analysis under the restriction of stochastic ordering. The first problem is that of estimating a survival function <(F)over bar (t)> under the restriction <(F)over bar (t)> greater than or equal to <(F)over bar (0)(t)>, all t, where (F) over bar (0)(t) is known. The second problem consists of estimating two unknown survival functions <(F)over bar ((t))(t)> and <(F)over bar ((2))(t)> when it is known that <(F)over bar ((1))(t)> greater than or equal to <(F)over bar ((2))(t)>, all t. The nonparametric maximum likelihood estimators in these problems were derived by Brunk, Franck, Hansen and Hogg and Dykstra. In the present paper we derive their large-sample distributions. We present two sets of proofs depending on whether or not the data are right-censored. When centered and scaled by n(1/2), the estimators converge in distribution to limiting processes related to the concave majorant of Brownian motion. The limiting distributions are not known in closed form, but can be simulated for the purpose of forming asymptotic point-wise confidence Limits.