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Advanced Statistics: Statistical Inference


  • The course is usually offered in the winter semester.
  • For passing the course and the exam, good knowledge in mathematics and statistics is required.
  • Usually, the following topics are dealt with in the course: Basic problems of statistical inference, point estimation, ML-, moment and Bayes estimators, hypothesis tests, tests for normally and binary distributed characteristics, variance and correlation analysis, confidence estimation, goodness-of-fit and independence tests, bootstrap and jackknife, density estimation

    Außerdem werden interaktive Tutorien angeboten. Hier werden Aufgaben zur Vorlesung unter Anleitung durch Studierende gerechnet. Die Tutorien werden in kleinen Gruppen durch Kommilitonen im höheren Semester abgehalten.

  • In addition to the lecture exercises are offered where mathematical problems of the lecture are discussed and solved. It is suggested that students prepare the tasks beforehand.

Contents and Goals

Advanced methods for parameter estimation and hypothesis testing are discussed. Students will learn about point- and intervall estimation and hypothesis testing, particulary parametric and non-parametric estimates and tests. 

Contents and Goals are:

  • Problems of statistical inference
  • Point estimation, Maximum Likelihood, Moments and Bayesian estimates
  • Hypothesis testing
  • Tests for normal and binary properties
  • Analysis of Variance and Correlation
  • Confidence estimation
  • Bootstrap and Jackknife
  • Non-parametric density estimation