EXTENDING THE RELATIONSHIP BETWEEN RIDGE-REGRESSION AND CONTINUUM REGRESSION

Recently, a close relationship has been established between ridge regression (RR) and a special case of continuum regression (CR). Attention was restricted to the usual positive range of values for the ridge parameter. This restriction identifies the trajectory lying between ordinary least squares (OLS) and partial least squares (PLS) regressions, leaving the trajectory between PLS and principal component regression (PCR) untouched. In this note we demonstrate that the relationship between CR and RR can be extended to the full range of methods, OLS <-> PLS <-> PCR, identified by the CR technique. For this purpose one has to admit a nonstandard variant of the RR technique in which the ridge parameter becomes negative.