Nonequivariant Simultaneous Confidence Intervals Less Likely to Contain Zero
提出一种构造同时置信区间的新方法，通过反转非等变假设检验并投影凸包，得到的区间比标准方法更少包含零，适用于独立同分布或可交换的随机变量。
Abstract We present a procedure for finding simultaneous confidence intervals for the expectations μ = (μ j ) n j=1 of a set of independent random variables, identically distributed up to their location parameters, that yields intervals less likely to contain zero than the standard simultaneous confidence intervals for many μ ≠ 0. The procedure is defined implicitly by inverting a nonequivariant hypothesis test with a hyperrectangular acceptance region whose orientation depends on the unsigned ranks of the components of μ, then projecting the convex hull of the resulting confidence region onto the coordinate axes. The projection to obtain simultaneous confidence intervals implicitly involves solving n! sets of linear inequalities in n variables, but the optima are attained among a set of at most n 2 such sets and can be found by a simple algorithm. The procedure also works when the statistics are exchangeable but not independent and can be extended to cases where the inference is based on statistics for μ that are independent but not necessarily identically distributed, provided that there are known functions of μ that are location parameters for the statistics. In the general case, however, it appears that all n! sets of linear inequalities must be examined to find the confidence intervals.