Estimation of Survival Functions under Uniform Stochastic Ordering
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一致随机序约束下的生存函数估计
- 研究问题
- 当两个生存函数之比随时间非增时，如何估计未知生存函数，并处理受约束非参数极大似然估计的不一致问题？
- 方法与思路
- 作者考察一致随机序约束下已有估计量，构造包含两种既有方法作为端点的单参数估计量族，并讨论内部成员选择。
- 材料陈述的贡献
- 摘要称多个未知生存函数的受约束极大似然估计一般也不一致，并以新的估计量族连接两种已有一致估计方法。
- 阅读关注点
- 应核对不一致结论的适用范围、估计量族各成员的性质，以及选择内部成员的启发式论证能否得到更严格支持。
- 阅读边界
- 仅据 OpenAlex 索引摘要，稿件版本未注明。摘要仅给出内部成员选择的启发式依据，未说明整个估计量族的一致性或最优性。
原文摘要
If S and T are survival functions for two life distributions, then S is said to be uniformly stochastically smaller than T, denoted by S ≪ T, if θ(x) ≡ S(x)/T(x) is nonincreasing in x on {x: T(x) > 0}. This ordering is transitive. Uniform stochastic ordering (USO) has found important applications in nonparametric accelerated life testing, among other areas. It has been shown that the nonparametric maximum likelihood estimator (NPMLE) of S under USO when T is known is inconsistent. Dykstra, Kochar Robertson derived the restricted NPMLE's of several unknown survival functions linearly ordered by USO. This article shows that these too are inconsistent in general. Rojo and Samaniego gave excellent ad hoc estimators of S and T when the other is known. Based on their idea for the one-sample problem, they gave two ad hoc estimators (one of them only implied) of S and T when they are both unknown. These are consistent, but they lack some desirable properties. This article introduces a one-parameter family of estimators that contains both of these estimators as extreme members. Some heuristic arguments are given to show that an interior member of this family is the appropriate one to choose.