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Statistical Tests and Estimators

Learning objectives

• knowledge of concepts of statistical estimation theory
• ability to autonomously develop estimators according to learned concepts
• knowledge of performance criteria for estimators, ability to evaluate estimators according to these criteria
• knowledge of established estimators in standard situations
• knowledge of concepts of statistical hypothesis testing theory
• ability to autonomously develop tests according to learned concepts
• knowledge of performance criteria for statistical tests, ability to evaluate test procedures according to these criteria
• knowledge of established tests in standard situations

Contents

• maximum likelihood estimation, method of moments, least squares estimators, L1 estimator
• classical performance criteria and robustness criteria for estimators
• decision theory: estimation problem as statistical decision problem
• standard estimators: estimation of expectation, variance, and regression parameters
• decision theory: statistical hypothesis testing s statistical decision problem
• Neyman-Pearson lemma
• parametric statistical tests: likelihood ratio test
• performance criteria for tests
• tests for standard situations: parametric and nonparametric tests for location and scale; goodness of fit tests

Prerequisites

There are no formal prerequisites for participation in the course. However, knowledge of statistics and mathematics at bachelor level is desirable.

Lecture and exercise documents

Script, exercises, sample solutions as well as a collection of formulas are available for download in Stud.IP in the respective semester. Examinations with sample solutions from previous semesters can be found at the end of this page.

Scope and evaluation

• lecture with 2 WCH and exercise with 1 WCH
• written exam
• 5 credit points

Dates

Lecture and exercise dates are announced via Stud.IP. The course takes places every second summer semester. Examination dates can be found on the website of the examination office.

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