Stepwise, also called stagewise, methods in fitting regression models have been extensively studied [Page 1450]and applied in the past 50 years, and they still remain an active area of research. In many study designs, one has a large number K of input variables and the number n of input–output observations (xi1, …, xiK, yi), 1 ≤ i ≤ n, is often of the same or smaller order of magnitude than K. Examples include gene expression studies, where the number K of genomic locations is typically larger than the number n of subjects, and signal or image reconstruction, where the number K of basis functions to be considered exceeds the number n of measurements or pixels. Stepwise methods are perhaps the only computationally feasible ways to ...