After successful completion of the course, students are able to

create and analyse models and their consequences  following mathematical principles

 

For that arealso further knowledge of measure theory and probability theory is required,

since in particular the theoretical properties of statistical models as well can be investigated in infinitely dimensional spaces.

 

Repetition from the theory of measure and probability of the elements thatare particularly important in mathematical models,

Parametric and non-parametric distribution families,

Decision theory as the basis for optimal decisionsInformation measures, learners and Bayesian models

Statistical Tests - Point & Area Estimation,Convergence properties and asymptotics of optimal procedures,

Multi-dimensional methods and statistics for stochastic processes

Self study with lecture notes, progress control by online quizzes, questions and feedback by forum or chat

 

Oral exam

Witting: Mathematische Statistik I Heyer: Theory of Statistical Experiments Lehmann: Testing Statistical Hypotheses Lehmann: Theory of Point Estimation Ferguson: Mathematical Statistics, a Decision-Theoretic Approach

 knowledge of probability theory and measure theory