Fortgeschrittene Methoden der Mathematischen Biometrie B (Hochdimensionale Statistik)

The lecture gives an introduction to high-dimensional statistics. Many estimation problems in modern statistics are high-dimensional, that is, the number of parameters to be estimated is much higher than the number of observations. A leading example is the (sparse) high-dimensional linear regression model, where the number of regressors (and thus the number of parameters) is potentially much larger than the number of data points. There are different statistical methods to estimate the unknown parameters in (sparse) high-dimensional linear models, among them the lasso and boosting. In the lecture, we develop basic theory for the lasso and (L2) boosting. Specifically, we derive theoretical results on the prediction, parameter and model selection consistency of these methods.