Introduction to Mathematical Statistics (Mathematische Statistik)

Dienstag 10:00-12:00 Uhr (M2)
Freitag 10:00-12:00 Uhr (M2)

Wegen eines Auslandsaufenthaltes zu Beginn des Semesters werden die ersten beiden Vorlesungen online stattfinden sowie voraussichltich aufgezeichnet und im Learnweb zur Verfügung gestellt.

This course will be held in English.

Moving from Probability Theory to Mathematical Statistics, the major novelty is the decision-theoretic aspect that comes into play because the focus is shifted from the analysis of a given model to the purpose of "explaining" a given set of random data, which are based on an unknown probability model, by picking, in a suitable sense to be described, the most plausible model from a given set. This course aims at laying the foundations for this task. It will start by providing some basics of decision theory and then proceed to describe the main notions and approaches to solve prototypical statistical problems of increasing complexity. Here are some keywords: point estimation, maximum likelihood principle, unbiased estimation, method of moments, sufficiency and completeness, Lehman-Scheffé theorem, linear regression, Gauss-Markov theorem, hypothesis testing, level-α tests, Neyman-Pearson lemma, one- and two-sided hypotheses, Gauss tests, t-test (heuristic derivation).