In the framework of regression, consider the set of regression submodels. By submodel, we mean on e or more response variables and a subset of the potential regressors. Imagine the submodels as a ponts in some space. How can we "project" these ponts onto a map so as to visualize and compare...

This article gives results specifically related to the last principal component. This linear combination of variables plays an important role when one tries to fit a hyperplane to a cloud of points. In data analysis, variables are often subject to a linear transformation. The results that we...

We examine in this paper various consequences of the Poincari separation theorem. First, Poincari's theorem is used to prove results establishing a constrainted principal component analysis, both at the sample and at the population level. Introduction of constraints in principal component...

In this paper, we discuss one of the reasons leading practitionners to the rejection of the Markowitz model and propose a new stastistical method to avoid this problem. To be more precise, we discuss the problem of statistical robustness of the Markowitz optimizer and show that the latter is not...