Mini-course “An introduction to high-dimensional statistics I” Professor Enno Mammen (Heidelberg University)
Professor Enno Mammen (Heidelberg University)
Program of course:
The linear model. Classic Theory. The lecture gives a short summary of least squares estimation in linear models. It summarizes classical distribution theory in models with normally distributed errors and it discusses asymptotic distribution theory for models with general error distributions.
Sparse high-dimensional linear models. The LASSO-estimator. The lecture introduces to the notion of a sparse high-dimensional linear model. The LASSO-estimator is discussed and its asymptotic performance in sparse high-dimensional models is analysed. A short discussion of the finite-sample shape of the LASSO-estimator is added.
Statistical procedures in high-dimensional linear models. Desparsified LASSO-estimators. Modifications of the LASSO-estimator are discussed that allow a complete asymptotic distribution theory. These estimators are called desparsified LASSO-estimator and they can be used for implementation in the construction of statistically valid confidence regions and tests. Extensions to models in nonparametric regression concludes the lecture series.