After successful completion of the course, students are able to...
define statistical models
define and check sufficiency
define estimators and their properties
construct maximum likelihood and moment estimators
apply the Cramér-Rao theorem
define confidence intervals and compute them for special distributions
define statistical tests
define errors of the first and second kind, level of significance and power of a test
cite the Neyman-Pearson theorem
construct likelihood ratio tests and evaluate their asymptotic distribution
give criteria for the existence of uniformly optimal tests
perform analysis of variance
cite the Fisher-Cochran theorem
describe and perform linear regression
use the chi square and Kolmogorov Smirnov tests
describe basic ideas of Bayesian statistics
Statistical models, estimators, confidence intervals, tests, analysis of variance, regression, Bayes methods
Self study with lecture notes, progress control by online quizzes, questions and feedback by forum or chat
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
