Students are required to select two of the five electives of specialization.
Details to the individual tracks can be found in the Module Descriptions (Modulbeschreibungen, in German).
This track provides a deep understanding for the theoretical and practical aspects of modern statistical methods. Students acquire the ability to formulate analytical solutions to statistical problems. They are knowledgeable of the current state of research and are prepared to further develop and apply statistical methods to independent academic activity or for qualification for a doctoral program. Students have the flexibility to determine the scope of their training in the theoretical and applied statistics and can explore several current research directions. The specialization track Statistical Inference consists of the following modules Applied Statistics, Current Research Topics in Statistics, Mathematical Statistics, Statistics of Stochastic Processes, Reliability Theory, and Modern Methods of the Statistics.
Advanced methods in the areas of the microeconometrics, panel data analysis and time series analysis are the major components of the econometrics specialization track.
In the module Microeconometrics students acquire a solid theoretical and application orientated knowledge of models and methods for the analysis of individual behavior using micro data for individuals, households and companies. Students are trained to judge empirical analyses critically based on micro data and conduct independent empirical investigations.
The module Econometric Analysis of Panel Data expands on this foundation and introduces fundamental concepts and methods for the analysis of panel data, with particular attention to applications of micro data sources. Students are trained in cutting edge research methods and prepared to conduct independent empirical investigations based on panel data as well as to critically judge existing studies.
The module Time Series Analysis focuses on econometric methods in the analysis of time series data and their applications. Students are trained in cutting edge research methods and prepared to conduct independent empirical investigations based on (mainly economical) time series data as well as to critically judge existing studies.
The module Econometric Analysis presents current econometric methods, which are necessary for the analysis of time series data. Students are trained to critically judge and appropriately use these procedures. The primary focus is on modelling multivariate stationary and not-stationary time series. Topics considered include unit root tests, Vector Autoregressive models, Cointegration, error correction models. Students are prepared to conduct independent empirical investigations on time series.
In the Project Seminar Econometrics module students have the opportunity to put their knowledge of econometric analysis to use. This module consists of the development of internal and external resources and empirical data preparation. Students learn how to translate econometric models into a framework, which can be estimated and empirically evaluated.
Quantitative Methods of the Financial Markets
This specialization track teaches the relevant statistic and econometric methods and models which are of importance in the analysis of financial markets. The range of topics covered includes the pricing of options and other derivatives, time series models such as ARIMA and GARCH, analysis of high frequency time series by means of point processes, and risk management models such as Value-at-Risk (VaR). The module is designed as an introduction to the statistical instruments of the financial and insurance industry, the quantitative methods of the financial system and statistical aspects of credit evaluation.
In the module Statistics of Financial Markets students acquire a comprehensive and application orientated knowledge of statistical methods used in the analysis of financial markets. Fundamental concepts such as option pricing, stochastic processes in discrete time, the Black Scholes options model and the current VaR methodology are discussed.
The module Econometric Analysis of Financial Markets is concerned with the statistical characteristics of financial market data as well as specialized econometric analysis methods. The core of this module includes the modelling of volatilities, the connection between prices, dividends and expected net yields, the analysis of high frequency financial market data as well as the empirical market microstructure analysis.
In the module Stochastics of the Financial Markets students acquire a deep understanding of the fundamental stochastic concepts for the analysis of financial markets. The focus is on concepts of risk theory as well as the mathematics of insurance.
The module Introduction to the Theory of Sampling gives an introduction to the area of survey statistics. The methodological foundations will be discussed as well as the most important sampling methods and the most important surveys are introduced. During the exercise sessions students will learn how to use statistical software packages and evaluate sampling methods on their own.
The module Advanced Methods in Survey Statistics builds on the foundations set in the introductory course and gives a broad overview over sophisticated methods of survey statistics, i.e. calibration and weighting, methods for variance estimation, panel-surveys, small area estimation, etc. Students will be equipped with strategies to solve problems in current surveys.
The module Nonresponse discuses different approaches to substitution of missing data (imputiation). The lecture Introduction to Bayes-Statistics and Multiple Imputation provides the students with the basic methodological knowledge of these techniques. During the lecture Treatment of Missing Values in Surveys different methods of imputation will be discussed and applied.
The core topic of the module Simulation and Sampling is the Monte-Carlo-Technique which is used frequently to evaluate sampling designs in the context of survey statistics. The simulation can be performed with different software packages. During the lecture Introduction to Monte-Carlo-Simulation the software package R will be used while SAS is introduced during the lecture Computational Statistics.
Statistics in the Life Science
The module Methodical Fundamentals of Biometrics introduces the fundamental models and methods of the Biometrics as well as their applicability in practice. Students are trained to formulate complex problems clearly and to make important decisions influencing analytic activities. The lectures provide a foundation of Biometrics with emphasis on methods, which are specific for applications in medicine (statistic evaluation of diagnostic tests, analysis of censored data (survival analyses), drop number planning for clinical studies, multiple testing, epidemiological study designs). In addition, students are exposed to a comprehensive introduction to topics in the Biometric specialization track (sequential and adaptive methods, multiple linear regression, false discovery rate). The application of these methods will be explained and illustrated by empirical examples.
The module Biometrics expands on this foundation and provides an application orientated knowledge of important models and methods of Biometrics. Students are trained in statistical analysis for decision making responsibilities within the pharmaceutical, medical and biometric industries. Lectures cover applied methods of the Biometrics, with a focus on providing biometric support for empirical studies. The focus of the module is on methods and applications of the Biometrics for clinical studies (phases I – III studies including regulatory aspects and „Good Clinical Practice “, group-sequential and adaptive Designs) as well as a selection from more specialized topics (multiple involution models inclusively beginnings for dependent data, multivariate procedures, statistic methods of bio computer science). The use of these methods is explained and illustrated using empirical examples.
The module Prognosis Models in Biometrics introduces elementary procedures for the analysis of medical survival data (Kaplan Meier procedure, log climb test, experimental design using drop number estimation with different complexity level, simple Cox model with constant covariates). Advanced methods (multiple Cox model, time-dependent covariates, Multistate models) are presented and a view on the correct modelling and analysis for dependent data („frailty models “) are given. The use of these methods is explained and illustrated using empirical examples.
The module Psychometrics deals with the particular methodological challenges arising when collecting and analyzing data in the field psychology. The module focuses on models for latent variables and nested data which often occur in the context of research in this field. The lecture Multivariate Methods in Psychology provides the students with a broad understanding of topics like specification and evaluation of measurement models, multilevel analysis as well as structural equation models with latent variables. During the seminar Trends in Psychological Methodology topics from the current literature will be discussed.