Methoden der Statistik

Learning and qualification objectives:

  • Introduction to classical and modern statistical methods
  • Gain knowledge how to model und evaluate statistical data
  • Acquire ability of applying and interpreting basic statistical procedures
  • Understand non-asymptotic results (oracle inequalities)


  • Mo. 09:15 - 10:45 in room 0'311 (RUD26) - D. Kreher
  • Fr. 09:15 - 10:45 in room 1'304 (RUD26) - D. Kreher


  • Fr. 11:15 - 12:45 Uhr in room 3.007 (RUD25) - E. Ziebell


  • Basic statistical concepts: parameter estimation, hypothesis testing, confidence regions
  • Linear model: generalized least squares method, Bayes estimator, ridge regression estimator, t-/F-test, ANOVA
  • Exponential families: Cramér-Rao efficiency, generalized linear model, oracle inequaliity
  • Model selection: AIC, BIC, oracle inequality for penalized model selection, LASSO
  • Classification: LDA-classifier, SV-classifier, kNN-classifier, RKHS and SVM


  • M. Trabs, M. Jirak, K. Krenz, M. Reiß: Statistik und maschinelles Lernen (Springer, 2021)
  • H.-O. Georgii: Stochastik. Einführung in die Wahrscheinlichkeitstheorie und Statistik (de Gruyter, 2007)
  • T. Hastie, R. Tibshirani, J. Friedman: The elements of statistical learning. Data mining, inference, and prediction (Springer, 2009)
  • E.L. Lehmann, G. Casella: Theory of point estimation (Springer, 1998)
  • S. Richter: Statistisches und maschinelles Lernen. Gängige Verfahren im Überblick (Springer, 2019)
  • S. Shalev-Shwartz, S. Ben-David: Understanding machine learning: From theory to algorithms (Cambridge University Press, 2014)
  • J. Shao: Mathematical statistics (Springer, 2003)