Simultaneous Confidence Intervals and Regions

Abstract Simultaneous confidence intervals constitute a confidence region for a vector of parameters, comprising individual intervals for the separate components, with a coverage confidence level of the simultaneous correctness of all the statements involved. The approach is delineated for multiple comparisons of treatment means with the methods of Bonferroni, Duncan, Scheffé, and Tukey, as specific examples. The applications of simultaneous confidence intervals to the inference of a therapeutic window or the reliability of composite systems necessitate the elucidation of multiple sets of simultaneous confidence intervals. Studies related to condensing infinite sets of simultaneous confidence intervals trigger a discussion on simultaneous confidence bands. Integrating the intrinsic information on the patterns or trends governing a set of simultaneous confidence intervals for the mean responses results in the methodology of range regression.