Continuum Regression is Not Always Continuous
本文发现连续回归方法得到的预测值可能随参数γ或校准数据不连续变化，并用真实数据举例，揭示了其与岭回归的关系是理解这一现象的关键。
SUMMARY Continuum regression (CR) is regression of a response y on that linear combination t γ of explanatory variables which maximizes r 2(y, t) var(t)γ, where γ is chosen from a continuum of candidates. CR includes several common methods as special cases: ordinary least squares, principal component regression, partial least squares and a modified ridge regression. We demonstrate that CR, despite its name, can yield a predictor that is a discontinuous function of γ and of the calibration data. We illustrate this with a set of real data. The relationship between CR and ridge regression is the key to understanding this phenomenon.