EXTENDING THE RELATIONSHIP BETWEEN RIDGE-REGRESSION AND CONTINUUM REGRESSION

Recently, a close relationship has been established between ridge regr ession (RR) and a special case of continuum regression (CR). Attention was restricted to the usual positive range of values for the ridge pa rameter. This restriction identifies the trajectory lying between ordi nary 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 bet ween CR and RR can be extended to the full range of methods, OLS <-> P LS <-> PCR, identified by the CR technique. For this purpose one has t o admit a nonstandard variant of the RR technique in which the ridge p arameter becomes negative.