Principal Components Analysis with Respect to Instrumental Variables Via Univariate Splines

Introducing univariate splines provides an approach for solving the PCAIV problem in the non linear case: That is to build a representation of the observations as near as an another study, presupposing that the link between the two studies’variables takes an additive form. The linear PCAIV (Bonifas et al., 1984) is then a particular case ofthe spline-PCAIV (Durand, 1989) in the following sense: The solution of the linear PCAIV belongs to the set of feasible solutions of the spline-PCAIV and will constitute the first step of the associated iterative algorithm. Moreover this method presents an extension to regression using additive splines and can be considered as a particular canonical analysis in one sense which is specified.