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Stepwise, also called stagewise, methods in fitting regression models have been extensively studied 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 ≤ in, 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 ...

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