Contents:

• Asymptotic analysis of M-estimators, especially of Maximum-Likelihood-estimators
• Bayes and Minimax-estimators
• Likelihood-ratio-tests: asymptotic analysis and examples (t-test, chi²-goodness-of-fit-test)
• Glivenko-Cantelli-theorem, Kolmogorov-Smirnov-test
• Differentiable statistic functionals and examples of applications (derivation of asymptotic results, robustness)
• Resampling methods on the basis of Bootstrap.

Contact time:

4 SWS / 60 h Lecture
2 SWS / 30 h Tutorials

Prerequisites (Contents):

The lecture "Stochastic Methods" from the Bachelor degree program in mathematics.

Frequency of occurence:

The lecture is given once per year, in the winter term.

KIS

OLAT

Contents:

• Basic theory of spatial point processes (marked point processes, intensity measure,...)
• Poisson process, Poisson cluster processes
• Basic theory of random closed sets
• Germ-grain models, in particular Boolean models
• Random tessellations

Contact time:

2 SWS / 30 h Lecture

1 SWS / 15 h Tutorials

Prerequisites (Contents):

Modul „Probability Theory“.

Frequnecy of occurence:

The lecture is irregularly given.

KIS

OLAT

Appointments upon prior arrangement. If you are interested in participating the seminar, please directly contact Prof. Dr. Claudia Redenbach via Email (claudia.redenbach@rptu.de). The kick-off meeting will take place in the first week of lectures.

KIS

OLAT

Contents:

• Linear regression models
• Parametric curve fitting
• Likelihood ratio tests
• Data adaptive model selection
• Analysis of Variance (ANOVA)
• Experimental design
• Stationary stochastic processes
• Autoregressive and ARMA-processes
• Parameter estimation and model selection for time series
• Trend and seasonality
• Forecasting by exponential smoothing and the Box-Jenkins method
• Linear filters

Contact time:

4 SWS / 60 h Lecture
2 SWS / 30 h Tutorials

Prerequisites (Contents):

Elementary probability theory and statistics (e.g. Praktische Mathematik: Stochastik)

Frequency of occurence:

The lecture is given once per year, in the summer term.

KIS

OLAT

Contents:

• Spatial point processes (in R² and R³)
• Point process models (Poisson process, hard-core and cluster processes, Gibbs processes) and their simulation
• Statistical methods for point processes
• Marked point processes and particle processes

Contact time:

2 SWS / 30 h Lecture

Prerequisites (Contents):

The lecture "Stochastic Methods" from the Bachelor degree program in mathematics.

Frequnecy of occurence:

The lecture is irregularly given.

KIS

OLAT

Inhalte:

Statistics of Financial Markets:

• Models and estimation procedures for financial time series (ARCH, GARCH and generalisations), Value-at-Risk
• Copulas and its applications for risk managementbased on multivariate data

Extreme Value Theory:

• Statistical methods to estimate the probability of extreme events or extreme quantiles

Contact time:

2 SWS / 30 h Lecture

Prerequisites (Contents):

The lecture "Regression and Time Series Analysis".

Frequency of occurence:

The lecture is irregularly given.

KIS

OLAT