Simultaneous hypothesis testing was a lively topic in the early 1960s, my graduate student years, and had been so since the end of World War II. Rupert Miller’s book Simultaneous Statistical Inference appeared in 1966, providing a beautifully lucid summary of the contemporary methodology. A second edition in 1981 recorded only modest gains during the intervening years. This was a respite, not an end: a new burst of innovation in the late 1980s generated important techniques that we will be revisiting in this chapter.
Miller’s book, which gives a balanced picture of the theory of that time, has three notable features:
1 It is overwhelmingly frequentist.
2 It is focused on control of α, the overall Type I error ...