Significance regression: a statistical approach to partial least squares
Tyler R. Holcomb, Håkan Hjalmarsson, Manfred Morari, Matthew L. Tyler · Journal of Chemometrics · 1997
This paper presents a formal framework for deriving partial least squares algorithms from statistical hypothesis testing. This new formulation, significance regression (SR), leads to partial least squares for scalar output problems (PLS1), to a close approximation of a common multivariable partial least squares algorithm (PLS2) under certain model assumptions and to more general methods under less restrictive model assumptions. For models with multiple outputs, SR will be shown to have certain advantages over PLS2. Using the new formulation, a significance test is advanced for determining the number of directions to be used. The prediction and estimation properties of SR are discussed. A brief numerical example illustrates the relationship between SR and PLS2. © 1997 John Wiley & Sons, Ltd.