Berwin's Problem

Research Report MRR98-049

Berwin's Problem

M.R. Osborne, Brett Presnell and B.A. Turlach

Abstract: The title Lasso has been suggested by Tibshirani [6] as a colourful description of a technique for variable selection which requires the minimization of a sum of squares subject to an l₁ bound on the solution components. This bound then has the role of the selection parameter. Here a descent method for solving the constrained problem is formulated, a homotopy method in which the constraint bound becomes the homotopy parameter is developed to completely describe the possible selection regimes, and it is suggested that modified Gram-Schmidt applied to the augmented design matrix provides an effective base for implementing the suggested algorithms.

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