BACHELOR THESES
Bachelor theses in Statistics consist of a description of new statistical methods and their application on specific data.

Registration
We would like to ensure that all students of the Economics and Management bachelor receive a topic for their theses within standard period of study. Therefore, allocation is made by the Office of the Dean of Studies via a centralized application procedure. Afterwards, the Office of the Dean of Studies will inform you about the institute which you were assigned to.

Assignment of Topics
We have prepared a selection of topics for students who were assigned to our institute. Topics for summer term 2020 as well as winter term 2020/21 will be assigned within a online meeting, which took place on Wednesday, 6th May 2020 at 16.15. Students who could not participate may find a list with current topics on our website.
TOPICS
We have arranged a selection of 27th topics from different areas.
In the following, you may find a list of currently available topics which may help for your choice. If a topic is no longer available, we will remove it from our website.
The descriptions of content as well as liturature references can be taken from the general overview which is linked above.

Models of Descriptive Statistics and Stochastics

Limits of Classic Linear Regression
Heteroscedasticity
In the least squares method it is assumed that the variance of the disturbance terms is constant. However, if the variance of the disturbance varies, the LS estimator is no longer
efficient. This can be proven with tests such as WhiteTest or Godfrey LM Test. Solutions are offered by heteroscedasticityresistant standard errors or the weighted LS method. If autocorrelation is also present, HAC (heteroscedasticity and autocorrelation consistent) estimators must be used. (This thesis is supervised in English).Introductory Literature:
 Jeffrey M. Wooldridge. 2013. Introductory econometrics: A modern approach. Nelson Education (Chap. 8 + 12)
 William H. Greene. 2012. Econometric analysis. Pearson Education (Chap. 9)
Specification tests: RESET
Consider the model specication of a linear regression model, where the independent regressors x_i are linearly related to the dependent variable y. This assumption about the functional form of a regression can be tested and these tests should be content of this work. The bestknown test is the socalled RESET test. In addition, for example, the Rainbow and the HarveyCollier Test can be presented. (This thesis is supervised in English).
Introductory Literature:
 Walter Krämer und Harald Sonnberger. 1986. The linear regression model under test. PhysicaVerlag Heidelberg (Chap. 4)
Endogeneity: Instrumental Variables
Consider a linear regression model, where a prerequisite for the consistency of the OLS estimator is that the independent variable x and the error term e are uncorrelated. If this assumption is violated, there is socalled endogeneity. One consequence is that the OLS estimator has a bias. The presence of endogeneity can be resolved through socalled instrumental variables, which are used in the Two Stage Least Squares (2SLS) in order to obtain a consistent estimate of the effect ß. (This thesis is supervised in English).
Introductory Literature:
 Jeffrey M. Wooldridge. 2013. Introductory econometrics: A modern approach. Nelson Education (Chap. 15)
 James H. Stock und Mark W. Watson. 2011. Introduction to Econometrics. Pearson Education (Chap. 12)
Simultaneous systems of equations
Consider a simple simultaneous system of equations, where it is characteristic is that y_1,t and y_2,t appear both on the left in an equation and on the right in an equation. Therefore, an endogeneity problem arises. Two problems should be explained in detail in this work: First, the problem of identification, i.e. under which circumstances gamma_1 and gamma_2 can be estimated. Second, one should introduce an estimator that works under endogeneity and estimates the coefficients of the system equation by equation. (This thesis is supervised in English).
Introductory Literature:
 William H. Greene. 2012. Econometric analysis. Pearson Education (Chap. 10)
 Fumio Hayashi. 2000. "Econometrics". Princeton University Press (Chap. 8)
 Jeffrey M. Wooldridge. 2010. Econometric analysis of cross section and panel data. MIT Press (Chap. 8 + 9)
Endogeneity: Generalized Method of Moments (GMM)
Endogeneity bias can lead to inconsistent estimates and incorrect inferences, which may provide misleading conclusions and inappropriate theoretical interpretations. GMM is a statistical method that combines economic data with the information in population moment conditions and is able to estimate all coefficients simultaneously. The idea behind GMM must be explained and then applied to solve the system. (This thesis is supervised in English).
Introductory Literature:
 William H. Greene. 2012. Econometric analysis. Pearson Education (Chap. 13)
 Jeffrey M. Wooldridge. 2010. Econometric analysis of cross section and panel data. MIT Press (Chap. 8)
 Fumio Hayashi. 2000. "Econometrics". Princeton University Press (Chap. 8)
 Jeffrey M. Wooldridge. 2001. "Applications of generalized method of moments estimation". Journal of Economic perspectives 15 (4): 87100

Specific Regression Models

Multivariate Methods
Analysis of Variance (ANOVA)
ANOVA is the extension of the t and ztests where the means of two samples (or a sample and population) are compared relative to the standard error of the mean or pooled standard deviation. ANOVA is best applied where more than two populations are meant to be compared. The different test procedures as well as the motivation of the various test statistics should be presented. (This thesis is supervised in English).
Introductory Literature:
 Alvin C. Rencher und William F. Christensen. 2012. Methods of Multivariate Analysis. John Wiley & Sons, Inc. (Chap. 6)
 Joseph F. Hair u. a. 2014. Multivariate Data Analysis. Pearson Education Limited (Chap. 14)
Factor Analysis
In factor analysis, we represent the p elements of the vector y as linear combinations of a smaller number of m random variables, where m< p, called factors. Like the original variables, the factors vary from individual to individual; but unlike the variables, the factors cannot be measured or observed. The existence of these hypothetical variables is therefore open to question. If the p elements of vector y are at least moderately correlated, the basic dimensionality of the system is less than p. The goal of factor analysis is to reduce the redundancy (needlessness) among the variables by using a smaller number of factors. Motivation for factor models, model definition and assumptions as well as the estimation procedure should be covered. (This thesis is supervised in English).
Introductory Literature:
 Alvin C. Rencher und William F. Christensen. 2012. Methods of Multivariate Analysis. John Wiley & Sons, Inc. (Chap. 13)
 Joseph F. Hair u. a. 2014. Multivariate Data Analysis. Pearson Education Limited (Chap. 3)
Cluster Analysis
In cluster analysis we search for patterns in a data set by grouping the (multivariate) observations into clusters. The goal is to find an optimal grouping for which the observations or objects within each cluster are similar, but the clusters are dissimilar to each other. To group the observations into clusters, many techniques begin with similarities between all pairs of observations. In many cases the similarities are based on some measure of distance. Other cluster methods use a preliminary choice for cluster centers or a comparison of within and betweencluster variability. The techniques of cluster analysis have been extensively applied to data in many fields, such as medicine, psychiatry, sociology, criminology, anthropology, archaeology, geology, geography, remote sensing, market research, economics, and engineering. (This thesis is supervised in English).
Introductory Literature:
 Alvin C. Rencher und William F. Christensen. 2012. Methods of Multivariate Analysis. John Wiley & Sons, Inc. (Chap. 15)
 Joseph F. Hair u. a. 2014. Multivariate Data Analysis. Pearson Education Limited (Chap. 8)
MASTER THESES
Master Theses in Statistics consists of a description of new statistical methods and their application on specific data. This is similar to bachelor theses. Furthermore, new statistical methods could be described in detail and more critically. Another option is to do an empirical study on a statistical problem.

Registration
For master theses allocation is made on student's requests. If you would like to write your master thesis at our institute, you may contact Prof. Dr. Sibbertsen by email.

Topic Assignment
Topics for master theses are very diverse. They range from methodical work (method presentation, method comparison, method development) to own empirical work (data collection and analysis) with references to all other economic elective courses.
Topic assignment takes place in coordination with you. We will gladly consider your suggested topics.
CONTACT FOR GENERAL QUESTIONS ABOUT YOUR THESIS
30167 Hannover