Sequential dimension reduction via Sliced Inverse Regression

In multidimensional data analysis, one has to deal with datasets made of n points in dimension p. When p is large, classical statistical analysis methods and models fail. The goal of this PhD thesis is to tackle this problem. Numerous dimension reduction techniques can be used, depending on the context: Principal Component Analysis (PCA) in the unsupervised case, discriminant analysis in the case of supervised classification, Sliced Inverse Regression in the regression context are some of the most standard and popular algorithms. The goal of this PhD is to study and extend the SIR methodology.