Nonparametric Maximum Likelihood Estimation of Survival Functions with a General Stochastic Ordering and Its Dual
研究在总体间存在任意偏序随机序时，如何利用其他总体数据来估计难以获取数据的总体的生存函数，并给出一种基于Fenchel对偶定理的算法来修正序违反，得到收敛于最大似然估计的结果。
This paper discusses estimation of survival functions under an arbitrary partial stochastic ordering of the underlying populations. This technique is especially useful when data are not easily acquired from one or more of the populations, but data from the other populations are available. Estimation of the ordered survival functions entails use of a Fenchel duality theorem that results in an algorithm to identify and resolve violations of the underlying ordering. The algorithm produces estimates which converge to the maximum likelihood estimates of the survivalfunctions given the underlying ordering. The method is illustrated by an example.