Rejoinder: Fisher Lecture: Dimension Reduction in Regression

摘要

I am grateful to all of the discussants for their comments which raise a number of important and insightful issues, and add significantly to the breadth of ideas. Following a few introductory comments on the need for a new regression genre that centers on dimension reduction, I turn to the discussants' remarks.rnThe development in the 1960s and early 1970s of diagnostic methods for regression produced a major shift in regression methodology. When a diagnostic produces compelling evidence of a deficiency in the current model or data it is natural to pursue remedial action, leading to a new model and a new round of diagnostics, proceeding in this way until the required diagnostic checks are passed. By the late 1970s this type of iterative model development paradigm was widely represented in the applied sciences and was formalized in the statistical literature by Box (1979, 1980) and Cook and Weisberg (1982). With the availability of desktop computing starting in the mid-1980s, it is now possible to apply in reasonable time batteries of graphical and numerical diagnostics to many regressions.