The application of regularisation to variable selection in statistical modelling

The aim of variable selection is the identification most important predictors that define response a linear system. Many techniques for use constrained least squares ( LS ) formulation in which constraint imposed 1-norm (the lasso), or 2-norm (Tikhonov regularisation), combination these norms elastic net). It always assumed must necessarily be imposed, but consequences its imposition have not been addressed. This assumption considered this paper and it shown correct application Tikhonov regularisation to problem min ? A x ? b 2 requires satisfy condition C . If satisfied, then solution with numerically stable error e between small. If, however, large. derived from refined normwise number problem. includes examples correlated variables illustrate theory.