Contribution to missing values & principal component methods

This manuscript was written for the Habilitation à Diriger des Recherches and it describes my research activities. The first part of this manuscript is named "A missing values tour with principal components methods". It first focuses on performing exploratory principal components (PCA based) methods despite missing values i.e. estimating parameters scores and loadings to get biplot representations from an incomplete data set. Then, it presents the use of principal components methods as single and multiple imputation for both continuous and categorical data. The second part concerns "New practices in visualization with principal components methods." It presents regularized versions of the principal components methods in the complete case and their potential impacts on the biplot graphical outputs.The contributions are part of the more general framework of low rank matrix estimation methods. Then, it discusses notions of variability of the parameters with confidence areas for fixed effect PCA either using bootstrap and Bayesian approaches.