Knowledge:

• Loss functions and risk minimization
• Standard inequalities from probability theory
• Non-parametric model assumptions e.g. via kernel methods
• Finite sample error bounds under common assumptions, e.g. smoothness or sparsity
• Penalized regression, including ridge regression and lasso
• Graphical lasso

Skills:

• Perform theoretical analyses of statistical methods under parametric or non-parametric model assumptions.
• Discuss the limitations of the models and methods covered
• Derive error bounds based on the theory covered
• Ability to interpret theoretical results in the context of practical data analysis, including how complex models with many covariates can be analyzed and the results interpreted

Competences:

• Analysis of complex regression models with a large number of covariates
• Translation between joint models and regression models 
• Translation of a scientific hypothesis into either a parametric or a non-parametric mathematical hypothesis