Estimation of Survival Functions Under Uniform Stochastic Ordering
本文研究了在均匀随机序约束下多个未知生存函数的非参数最大似然估计的不一致性，并引入一族包含已有估计的估计量，通过启发式论证推荐内部成员作为合适选择。
Abstract 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.