Simultaneous Confidence Intervals and Regions Chapters uri icon

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abstract

  • AbstractSimultaneous 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, ScheffĂ©, 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.