Confidence Bounds for Normal Means Under Order Restrictions, With Application to Dose-Response Curves, Toxicology Experiments, and Low-Dose Extrapolation
针对有序正态均值，提出利用顺序约束的置信界计算方法，比传统方法更精确，可用于评估毒素安全性及低剂量外推中的虚拟安全剂量。
Abstract Suppose that y 1, …, yk are normal random variables with ordered means u 1 ≤ u 2 ≤ … ≤ uk . A confidence bound is found for each ui that takes advantage of the ordering. The upper and lower bounds are the maximum and minimum values of x such that the hypotheses that x < ui and ui < x are accepted by their respective likelihood ratio tests. These bounds are often more precise than the usual bounds and can be used to determine the safety of a toxin and to bound the virtual safe dose in a low-dose extrapolation. Simultaneous intervals for u 1, …, uk are also derived.