Multiple confidence sets based on stagewise tests
Abstract Recent years have seen suggested constructions of multiple confidence sets related to stagewise multiple tests by some authors. These methods are a type of mixture between test and confidence interval methods, because confidence interval statements are made only for some parameters, whereas test statements for fixed parameter values are made for the other parameters. In this article I define a concept—confidence directional set—giving a confidence bound for one parameter, which may depend on other parameters. Using this concept, one can construct multiple confidence sets, which are always confidence set statements and not test statements for fixed parameter values. The confidence sets correspond exactly to stagewise tests, which is theoretically appealing. Special examples of the general technique are given for the independent test statistic case and for comparison of a number of treatments to a control in the case of normally distributed observations with the same variance.