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Mini-course “An introduction to high-dimensional statistics II” Professor Enno Mammen (Heidelberg University)

Professor Enno Mammen (Heidelberg University)

On September 30 - October 1 professor Enno Mammen delivered a series of lectures on 'An introduction to high-dimensional statistics'.

Program of course:

Lecture 4. Complexity penalized least squares estimators.In this lecture penalized least squares estimators are discussed that have a penalty measuring the complexity/dimension of the model. An example are BIC-penalties. Theory is presented that  shows that for sparse linear models such estimators achieve optimal rates. In contrast to the LASSO-estimator no assumptions on the design matrix are needed.

Lecture 5. Mixing least squares estimators, sparsity pattern aggregation and exponential screening.The estimators of Lecture 4 can be described as two-step estimators where in the first step a model isselected and in a second step an estimator adapted to this model is chosen. In this lecture we discussin a class of models and their weights correspond to an estimated measure of the fit of the correspondingmodel. The lecture discusses recent adaptations of this idea to high-dimensional sparse settings. The course concludes with the discussion of some points of Lecture 3.