SD-205: Advanced Statistics

graduate course, Télécom Paris,

In many situations, the data available to the statistician are so complex that, at least in the first analysis, they escape any parametric modelling. The objective of this course is to present less rigid statistical techniques, as well as the theoretical issues inherent in their implementation: the counterpart of the increased flexibility of non-parametric approaches lies in the risk of “over-fitting” the model to the data. Through examples, the “minimax” perspective for non-parametric estimation, the “bias/variance” trade-off depending on the “complexity” of the model, and the statistical learning paradigm, “empirical risk minimization”, will be discussed.