Lecturer: Michael Vogt

Excercise: Manuel Rosenbaum

General Information

Language	Deutsch/Englisch
Lectures	4 h
Excercises	2 h

Lectures s. Moodle
Excercises s. Moodle
Exam s. Moodle

General Information:

Target Audience: 

• Master Mathematische Biometrie
• Master Wirtschaftsmathematik
• Master Finance
• Master Mathematik

Course Prerequisites:	Elementary Probability Calculus and Statistics
Exam:	Exam dates and further information will be posted on Moodle.

Contents

• The lecture gives an introduction to asymptotic statistics. In mathematical statistics, many theoretical results are asymptotic in nature. Hence, convergence concepts such as convergence in probability, almost sure convergence and convergence in distribution play a very important role.
• The first part of the lecture introduces basic concepts of stochastic convergence. It sheds some light on the connection between them and uses them to derive laws of large numbers as well as central limit theorems.
• The second part of the lecture uses the introduced convergence concepts to analyze the convergence behaviour of certain classes of estimators. Examples are the class of M-estimators (which includes many basic estimators such as least squares, maximum likelihood, GMM, etc.) and the class of nonparametric kernel estimators (which can e.g. be used to estimate densities and regression functions).

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Literature: 

• van der Vaart, Asymptotic Statistics, Cambridge University Press