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• Individual Writing Consultation

The Individual Writing Consultation allows you to meet with a consultant to work collaboratively on a particular writing task or assignment. The task may include, but is not limited to, theses, dissertations, scientific articles, course papers, academic application letters, research proposals, etc. 

In our sessions...

• we will discuss your questions and concerns about academic writing in German and English as a second or foreign language and develop possible solutions together,
• we support you in understanding the writing task and the subject-specific guidelines for scientific papers,
• we teach techniques and strategies that help you to organize your work and writing process
• we provide specific feedback on structural and linguistic aspects of your text,
• we support you with concrete problems that arise when writing in a foreign language, such as questions about sentence structure and scientific style,
• we provide materials with which you can continue working independently

What should the writer consider beforehand?

Please bring your writing task and your text or parts of your text to the writing consultation.

Inform yourself about the subject-specific requirements for scientific work in your area of study and bring along relevant guidelines, etc.

Please contact us at least 24 hours before an appointment in case you cannot attend.

To set up an appointment, please send us an E-Mail. Each session lasts between 30 and 45 minutes.

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The Institute for Applied Mathematics is devoted to the mathematical treatment of practical issues from the fields of natural, engineering and economic sciences. This involves mathematical modelling, theoretical studies and numerical approximations.

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Application Information and Documents

related to our study courses

Approximately 125 students are admitted to the bachelor's programme in architecture each year in the winter semester. The course is admission restricted. The numerus clausus (NC) is determined as a procedural grade during the admission procedure and is therefore not yet fixed at the beginning of the application procedure.

No other documents (such as proof of internships or an application folder) are required for the application apart from the regular application documents. Furthermore, no selection tests or job interviews are carried out.

In the consecutive Master's programme in Architecture and Urban Development, 75 places are awarded annually in the winter semester. The course is admission restricted. Admission is regulated by the Regulations on Admission and Admission. The selection decision is made by a selection committee on the basis of the submitted application documents.

Please note that in addition to the regular application documents, an application folder and proof of internship must be submitted. The application folder includes a letter of motivation with a maximum of 4,500 characters and up to 12 pages of work samples DIN-A3. Deviating from the admission regulations, the folder can also be submitted in DIN-A4 with a maximum of 24 pages or in special formats (not larger than DIN-A3).

In the bachelor's degree program, a good 80 students are admitted to the program each winter semester. The course of study is admission restricted. In the course of the admission procedure, the numerus clausus (NC) is determined as a procedural grade and is therefore not fixed at the beginning of the application procedure.

This information is intended to provide you with guidance and assistance in preparing your application documents. The information consists of extracts from the admission regulations and explanations.

In the Master's programme, 20 students are admitted each year in the winter semester and 10 in the summer semester. Admission to the consecutive Master's programmes is regulated by the Regulations on Admission and Admission for the respective Master's programme.

Admission to the Master's programme in Landscape Architecture requires that the applicant

• has obtained a Bachelor's degree or equivalent in landscape architecture and environmental planning or in a closely related field of study at a German university or at a university belonging to one of the Bologna Signatory States, or
• has obtained an equivalent degree in a closely related subject at another foreign university. Equivalence is determined in accordance with the evaluation proposals of the Central Office for Foreign Education at the Permanent Secretariat of the Standing Conference of Ministers of Education and Cultural Affairs.
• If the previous Bachelor's degree course has not yet been completed at the time of application, you can still apply. However, at least 150 credit points must be documented in your grade sheet by the application deadline.

The following documents must be attached to the application:

• Application for admission or enrolment at Leibniz Universität Hannover
• Certificates and supporting documents in certified copy
• curriculum vitae
• letter of motivation (maximum 5 pages): Why do you want to study at Leibniz Universität Hannover? What knowledge from your first degree qualifies you for this course? What motivation do you have for scientific and design work? Why will this course of study qualify you for your future professional goals? What are the focal points of your bachelor's degree course or perhaps not? (Please give reasons for this.) Which focal points do you want to set in your Master's degree course or perhaps not?
• Work samples (up to 10 pages): Show your specific talents and interests for the course with a selection of your previous work. Please indicate which part you have completed, if these work samples refer to group work.
• Applicants from non-German-speaking countries must enclose proof that they have passed a German language test for admission to higher education with at least DSH-2.

Application

Application is possible for the winter and summer semester. The application deadline for applicants from Germany and other European countries is 15 July and 15 January. For applicants from non-EU countries, the application period ends on 31 May or 30 November for the coming semester.

Admission requirements

This information is intended to provide you with orientation and work assistance in preparing your application documents. The information consists of extracts from the admission regulations and explanations. The legal basis for admission to the Master's programme is the Admission Regulations Master of Science Environmental and Regional Planning .

Prerequisite for admission to the Master's programme in Environmental and Regional Planning is that the applicant:

• has obtained a Bachelor's degree or equivalent in landscape architecture and environmental planning from a German university or a university belonging to one of the Bologna signatory states, or in a closely related field of study
• has obtained an equivalent degree in a closely related subject at another foreign university. Equivalence is determined in accordance with the assessment proposals of the Central Office for Foreign Education at the Permanent Secretariat of the Standing Conference of Ministers of Education and Cultural Affairs of the Länder in the Federal Republic of Germany (www.anabin.de).
• Curriculum vitae
• Letter of motivation (maximum 3 pages and up to 10 pages of samples of work) setting out the following:
• on the basis of which specific talents and interests the applicant considers himself/herself particularly suitable for this course of study,
• to what extent this course of study qualifies the applicant for his or her professional goals,
• the extent to which she or he is capable of scientific or method-oriented, planning work
• the extent to which he or she has a sound knowledge of the scientific fundamentals or basic knowledge from his or her first degree, and
• whether she or he would like to study the major nature conservation and landscape planning or the major regional planning.

Applicants for the Major Regional Planning (Territorial Development) whose native language is not English must demonstrate knowledge of English at least at language level B2. For details of the proof see: http://www.fsz.uni-hannover.de/de-nachweise.html .

Notes on the approval procedure

The selection committee for the Master's programme in Environmental and Regional Planning would like to provide support for the admission procedure with the following information:

1. definition of "closely related" programmes

Anyone with a degree other than e.g. Sc. landscape architecture / landscape planning / environmental planning can in principle also apply for the Master of Environmental and Regional Planning (Major Regional Planning). The previous degree should have a certain proximity to the subject area of the Major Regional Planning. The review is carried out on a case-by-case basis, i.e. we are available for information. As a rule of thumb for the close professional relationship, it can be taken that within the course of studies there must be basic knowledge in the areas of regional development and spatial and environmental planning. Admission is open to those who can demonstrate sufficient knowledge in the fields of urban and regional planning, spatial planning, environmental planning, geography with a spatial development focus (Urban and Regional Planning, Town and Country Planning, Environmental Planning, Geography (with Spatial Development focus).

Should some of these courses not have been represented in the previous course, admission can still be granted on the condition that courses determined by the admissions committee must be made up for. These conditions are issued with the notification of admission. A maximum of 12 ECTS is required in order not to influence the course of the Master of Environmental and Regional Planning.

2. letter of motivation and samples of work

The letter of motivation and the work samples serve to present your qualifications for the study location Hannover, so take this opportunity to do so. We do not measure the letters of motivation according to quantity, but exclusively according to quality. Therefore, it is imperative that the maximum number of pages is observed. The Admission Regulations make it important that the above five points are met by the letter, so use this as a guide. For the work samples, you should enclose excerpts from your Bachelor thesis or other work from your previous studies, but here too, you should adhere to the maximum number of pages. It is recommended to include a summary of the bachelor thesis and another sample of your work. Translated with www.DeepL.com/Translator (free version)

An application is possible for the winter and summer semester. The application deadline for applicants from Germany and other European countries is 15 July and 15 January. For applicants from non-EU countries, the application period ends on 31 May or 30 November for the following semester.

• has obtained a Bachelor's degree or equivalent qualification in landscape architecture and environmental planning or in a closely related field of study at a German university or at a university belonging to one of the Bologna signatory states, or

Applicants from non-German-speaking countries must prove that they have sufficient knowledge of the German language at language level C1 in order to study Nature Conservation and Landscape Planning.

1. Definition of "closely related" programmes

Those who have a degree other than e.g. Sc. landscape architecture / landscape planning / environmental planning can in principle also apply for the Master of Environmental and Regional Planning (Major Nature Conservation and Landscape Planning). The previous degree should have a certain proximity to the subject area of nature conservation and landscape planning. The review is carried out on a case-by-case basis, i.e. we are available for information. As a rule of thumb for the close professional relationship, it can be taken as a rule of thumb that environmental and spatial planning as well as landscape ecology contents must be represented within the degree course. In principle, admission is granted to those who can prove that they have completed at least 8 ECTS in the field of environmental and spatial planning, 8 ECTS in the field of landscape ecology and nature conservation and 8 ECTS in the field of plant ecology and vegetation science 4 SWS. If some of these courses were not represented in the previous course of study, admission can still be granted under the condition that courses determined by the admissions committee have to be made up for. These conditions are issued with the letter of admission. A maximum of 12 ECTS is required in order not to influence the course of the Master of Environmental and Regional Planning.

The letter of motivation and the work samples serve to present your qualifications for the study location Hannover, so take this opportunity to do so. We do not measure the letters of motivation according to quantity, but exclusively according to quality. Therefore, it is imperative that the maximum number of pages is observed. The Admission Regulations make it important that the above five points are met by the letter, so use this as a guide. For the work samples, you should enclose excerpts from your Bachelor thesis or other work from your previous studies, but here too, you should adhere to the maximum number of pages. It is recommended to include a summary of the bachelor thesis and another sample of your work.

• B.Sc. Technical Education Rules governing the selection procedure
• M.Sc. Teaching Profession at Vocational Schools Regulations on access and admission

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Environmental Engineering - Track Resources and Environment (Master of Science, Double Degree)

Part-time study is optional.

German HZB:  none International application: English C1  Find out more

Stay abroad possible, but not obligatory.

Short Description

Whether natural disasters and climate change, raw material shortages or disturbed ecosystems – the challenges of protecting the environment and our resources are global in scale. The “Resources and Environment” specialisation in the master’s degree programme in Environmental Engineering therefore focuses on forward-looking environmental scientific and technical solutions as well as the sustainable use of finite resources in an international context. The specialisation can be studied entirely in English.

 “Resources and Environment” offers you a unique combination of key content from the specialist disciplines of civil and environmental engineering, geodesy, mechanical engineering, and environmental and landscape planning. Your choice of specialisation, (optional) stay abroad, a practical project and topics such as green entrepreneurship will enable you to prepare specifically for a variety of career paths on the global labour market.

 Another attractive option is to pursue the double degree programme with the renowned Tsinghua University in China: by completing a second master’s degree, you will acquire additional specialist qualifications while gaining an insight into the world of academia and work in China, establishing contacts and developing your intercultural skills in the process.

• Further information for students on the website of the Faculty of Civil Engineering and Geodetic Science

Course Content

• Environment
• Circular Economy
• Water Resources Management
• Renewable Energies
• Hydrochemistry and -biology
• Meteorology and Climatology

During the first two semesters, the specialisation involves taking compulsory and elective modules that enable you to expand your specialist knowledge of engineering, mathematics and science. In the third semester, you choose a research-oriented (interdisciplinary) project or a practical project outside of the university to suit your strengths and future career plans. Students also have the option of studying abroad in the third semester. The fourth semester is mainly set aside for the completion of a master’s thesis

Besides gaining professional expertise, you will also learn the methods needed to solve engineering assignments effectively and in interdisciplinary contexts, and to analyse the results. During the programme, you will also develop the skills required to engage in interdisciplinary cooperation in an international environment.

• Creativity and imagination
• A keen sense of responsibility
• Assertiveness and eagerness to take decisions
• Enjoyment of technical, mathematical and scientific issues
• Knowledge of English

After graduating, a wide range of career opportunities will be open to you, especially on the international job market:

• Public sector (national and international specialist agencies)
• Consultant engineer (planner, environmental process engineer, project control)
• Research & development (industrial research, higher education institutions, research facilities)
• Industry (e.g. compliance officer / environmental officer, environmental engineer for aspects regarding REACH, emissions control officer, environmental process engineer)
• Utilities and waste management (e.g. water, waste water, recycling or energy management)
• Technical cooperation (GIZ)
• NGOs and environmental associations

Admission Requirements

he following documents are required for the application:

• University entrance qualification (eg "Abiturzeugnis" or high school diploma). Not applicable if you are currently studying at Leibniz University Hannover.
• Certificate of completion of the Bachelor''s degree programme (if already available). If you are currently studying at Leibniz University Hannover, just send a simple copy.
• Complete and current grades of the previous study with details of the credit points and the average grade with signature and stamp (if the diploma is not yet available). In the case of a programme with a total score of 180, at least 150 credit points must be proven; in the case of a programme with a total score of 210, at least 180 credit points must be proven.
• Curriculum vitae in English language.
• Applicants who have neither a German higher education entrance qualification nor have obtained their Bachelor''s degree from a German university must also have sufficient knowledge of the English language at the C1 level ( Details on language certificates ).

For master''s degree programmes with unrestricted admission , all applicants who fulfil the admission requirements will be admitted a university place. The exact admission requirements can be found in the admission regulations:

• Admission and special language Regulations Degree Programme Environmental Engineering
• Admission and special language Regulations Degree Programme Environmental Engineering (English translation)

Application Deadlines

First-year students from Germany and the EU

• June 1st – July 15th of the year for the winter semester
• December 1st – January 15th of the year for the summer semester

First-year students from non-EU countries ( VPD from uni-assist is required )

• April 15th – May 31st of the year for the winter semester
• October 15th – November 30th of the previous year for the summer semester

Students resuming their studies and transfer students from Germany and the EU (application in a higher semester)

Students resuming their studies and transfer students from non-EU countries (application in a higher semester)

• October 15th – November 30th of the previous year for the summer semester  

Joint degree programme with Tsinghua University, China The “Resources and Environment” specialisation enables you to add an international element to your studies: the double degree programme uniquely combines the strengths in research and teaching at Leibniz Universität Hannover and Tsinghua University in China. In addition to earning a Master’s degree at Leibniz Universität Hannover, you will be awarded a Master’s degree from Tsinghua Shenzhen International Graduate School. Practical phases, language courses and intercultural training courses are all part of the curriculum. Thanks to the academic and practical experience you will gain in both Germany and China, you will have the special skills required to pursue a career in an international environment after completing your double degree.

Procedure (standard course duration: 6 semesters): If you are enrolled through Leibniz Universität, you will spend your first year in Hannover. In the second year, you transfer to Tsinghua Shenzhen International Graduate School, where you initially take modules. A practical phase offers you insights into the world of work in China. You write a master’s thesis at each of the two universities. The double degree programme has a winter intake. A separate application is required for admission to this programme. The deadline for applying for the double degree programme is November 30th for applicants from non-EU countries and on January 15th for applicants from EU countries.

Find out more

Do you have questions about studying? We are happy to help!

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We are pleased that you would like to write your bachelor/master thesis at our institute. On this website you may find information about topics, registration and general guidelines. We wish you much success!

Bachelor Theses

Master theses, notes for theses, contact for general questions about your thesis.

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

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.

We have prepared a selection of topics for students who were assigned to our institute. You can find a list with all current topics on our website. 

Topics for summer term 2024 as well as winter term 2024/25 will be assigned as desired within the available topics. Therefore, please contact the office with your desired topic by email.

As soon as you have told us about your chosen topic, we will reserve it for you.

We have arranged a selection of topics from different areas.

In the following, you may find a list of currently available topics which may help for your choice.

Heteroskedastizität

Im klassischen linearen Regressionsmodell wird eine konstante Varianz der Fehlerterme angenommen. Bei sich verändernder Varianz ist der Kleinste-Quadrate-Schätzer nicht mehr effizient. Getestet wird dies z.B. mit dem White-Test oder dem Breusch-Pagan Test (Original oder Koenkers Version). Als Lösung werden Heteroskedastizität-robuste Standardfehler oder die Gewichtete-Kleinste-Quadrate-Methode genutzt. Falls gleichzeitig Autokorrelation vorliegt, finden sogenannte HAC-Schätzer Anwendung (heteroscedasticity and autocorrelation consistent).

Einstiegsliteratur:

• J.M. Wooldridge. Introductory econometrics: A modern approach. Nelson Education, 2013 (Kap. 8 + 12)
• W.H. Greene. Econometric analysis. Pearson Education, 2012 (Kap. 9)

Endogenität

Im klassischen linearen Regressionsmodell ist eine Voraussetzung für die Konsistenz des OLS-Schätzers, dass die Kovarianz zwischen der Regressormatrix und dem Fehlerterm Null ist. Falls diese Annahme verletzt ist, liegt sogenannte Endogenität vor. Eine Folge davon ist, dass der OLS-Schätzer einen Bias besitzt. Eine Möglichkeit, um mit Endogenität umzugehen,ist die Verwendung von sogennanten Instrumentalvariablen. Diese werden mithilfe des Two Stage Least Squares (2SLS) Verfahrens geschätzt, um eine konsistente Schätzung der Koeffizienten zu erlangen. Das Thema kann um eine weitere Lösungsmöglichkeit für das Endogenitätsproblem erweitert werden: Das Prinzip der generalisierten Momentenmethode (Generalized Method of Moments, GMM) liegt in der Festlegung von Bedingungen für die Momente der unterstellten Verteilung der Störterme des Modells. Die zu schätzenden Parameter werden so gewählt, dass sie möglichst gut im Einklang mit den Bedingungen stehen.

• J.H. Stock und M.W. Watson. Introduction to Econometrics. Pearson Education, 2011 (Kap. 12)
• J.M. Wooldridge. Introductory econometrics: A modern approach. Nelson Education, 2013 (Kap. 15)
• W.H. Greene. Econometric analysis. Pearson Education, 2012 (Chap. 13)
• J.M. Wooldridge. “Applications of generalized method of moments estimation”. In: Journal of Economic perspectives 15.4 (2001), S. 87–100

Simultane Gleichungssysteme

Ein einfaches simultanes Gleichungssystem lässt sich dadurch charakterisieren, dass die abhängige Variable in der einen Gleichung als erklärende Variable in der anderen Gleichung vorkommt und umgekehrt. Daher entsteht ein Endogenitätsproblem. Zwei Probleme sollen in dieser Arbeit näher erläutert werden: Zum einen das Problem der Identifikation, d.h. unter welchen Umständen können die Koeffizienten beider Gleichungen geschätzt werden. Zum zweiten sollen Schätzer vorgestellt werden, die unter Endogenität funktionieren und die die Koeffizienten des Systems Gleichung für Gleichung schätzen.

• W.H. Greene. Econometric analysis. Pearson Education, 2012 (Kap. 10)
• F. Hayashi. “Econometrics”. In: Princeton University Press (2000) (Kap. 8)
• J.M. Wooldridge. Econometric analysis of cross section and panel data. MIT Press, 2010 (Kap. 8+9)

Treatment Effects

Beim Schätzen von durchschnittlichen Treatment Effects geht es darum den Effekt verschiedenster Maßnahmen wie z.B. einer Weiterbildung zu analysieren. Insbesondere besteht die Frage wie man diese Effekte möglichst genau messen und kausal interpretieren kann, falls keine komplett randomisierten Experimente durchgeführt wurden. Für diesen Fall können Matching Verfahren angwendet werden um möglichst ähnliche Einheiten in der Treatment- und der Kontrollgruppe miteinander zu vergleichen. In dieser Arbeit sollen die zwei prominentesten Matching Verfahren und ihre Eigenschaften vorgestellt worden: Covariate Matching und Propensity Score Matching. Beim Covariate Matching werden verschiedene Einheiten basierend auf ihren beobachtbaren Eigenschaften miteinander gematched. Währenddessen werden beim Propensity Score Matching die Einheiten basierend auf der Wahrscheinlichkeit, dass sie in die Treatment Gruppe gehören, gematched.

• G. Cerulli. Econometric evaluation of socio-economic programs. Springer, 2015 (Chap. 2)
• J.M. Wooldridge. Econometric analysis of cross section and panel data. MIT Press, 2010 (Chap. 21)

Random Forests

Entscheidungsbäume stellen ein leicht zu interpretierendes nichtparametrisches Verfahren dar. Allerdings sind sie in der Praxis oft zu variabel, weswegen meist auf eine Erweiterung, die sogenannten Random Forests zurückgegriffen wird. Diese basieren auf der Idee des Bootstraps. Aus der ursprünglichen Stichprobe wird mit Zurücklegen eine neue Stichprobe gezogen, für die dann ein neuer Entscheidungsbaum bestimmt wird. Dabei wird in jedem Schritt zufällig ausgewählt auf Grundlage welcher Regressoren Entscheidungen getroffen werden können. Dieser Vorgang wird viele Male wiederholt und die Vorhersagen der so entstandenen Bäume werden durch Durchschnittsbildung zu einem Modell zusammengefügt. Einstiegsliteratur:

• G. James u. a. An introduction to statistical learning. Springer, 2013 (Kap. 8)
• L. Breiman. “Random forests”. In: Machine learning 45.1 (2001), S. 5–32
• E. Scornet. “On the asymptotics of random forests”. In: Journal of Multivariate Analysis 146 (2016), S. 72–83

Das Perzeptron stellt den Grundbaustein moderner neuronaler Netze dar und wird zur Klassifikation verwendet. In seiner grundlegenden Funktionalität kommt das Perzeptron dem multiplen linearen Regressionsmodell gleich. Im Bereich der neuronalen Netze werden die unabhängigen Variablen des Modells als Eingabe in das Perzeptron interpretiert, welche abhängig von den gelernten Gewichten des Perzeptrons zu einer bestimmten Ausgabe führen. Das Lernen der Gewichte erfolgt über einen iterativen Trainingsprozess, dessen Funktionsweise und Limitationen im Rahmen dieser Arbeit vorgestellt werden sollen. In der Arbeit soll weiter auf das Problem der linearen Separierbarkeit der zu klassifizierenden Daten eingegangen und Lösungsmöglichkeiten wie das mehrlagige Perzeptron oder der Maxover-Algorithmus vorgestellt werden.

• W. Ertel und N.T. Black. Grundkurs K¨unstliche Intelligenz. Springer, 2016 (Kap. 8.2)
• C.M. Bishop u. a. Neural Networks for Pattern Recognition. Oxford University Press, 1995 (Kap. 3.5)
• F. Rosenblatt. “The Perceptron: A Probabilistic Model for Information Storage and Organization in the Brain”. In: Psychological review (1958), S. 386

Hauptkomponentenanalyse

Die Hauptkomponentenanalyse, oder auch Principal Component Analysis (PCA), dient zur Identifizierung der Varianz-Kovarianz Struktur mittels Linearkombinationen aus den ursprünglichen Variablen. Die generelle Intention dieses Verfahrens dient der Komprimierung der Daten und der Interpretierbarkeit dieser. Bei der Anwendung der Hauptkomponentenanalyse werden häufig Zusammenhänge offengelegt, die vorher nicht offensichtlich sind und daher eine neue Interpretation der Datenstrukturen und Zusammenhänge innerhalb des Datensatzes ermöglicht. Aus diesem Grund wird die Hauptkomponentenanalyse hauptsächlich zur Erkennung von Beeinflussungsmustern und -strukturen in hochdimensionalen Datensätzen besonders im Bereich der Finanzwissenschaft, Data-Mining, Bioinformatik und der Umweltforschung eingesetzt.

• R.A. Johnson, D.W. Wichern u. a. Applied multivariate statistical analysis. Prentice Hall, NJ, 2002 (Chap. 8)
• A.J. Izenman. “Multivariate regression”. In: Modern Multivariate Statistical Techniques. Springer, 2013, S. 159–194 (Chap. 7)
• W.J. Krzanowski. Recent advances in descriptive multivariate analysis. Clarendon Press, 1995 (Chap. 5)
• M. Ringn´er. “What is principal component analysis?” In: Nature biotechnology 26.3 (2008), S. 303

Faktorenanalyse

Die Faktoranalyse behandelt multivariate beobachtete Variablen die zumeist von gleichen oder ähnlichen unterliegenden Variablen beeinflusst werden. Ähnlich wie die zu analysierenden Variablen sind auch die zugrundeliegenden Faktoren unterschiedlich für jedes beobachtete Individuum. Allerdings sind die zugrundeliegenden Faktoren unbeobachtbar. Jeder Faktor der verwendet wird erklärt einen Teil der Varianz in den beobachteten Variablen und wird danach geordnet, wie hoch der Anteil der erklärten Varianz von den einzelnen Faktoren ist. Das Ziel der Faktoranalyse ist die Dimensionsreduktion der analysierten Variablen. In der Arbeit sollen vor allem auf die Motivation für Faktormodelle, die Modelldefinition und Annahmen sowie Möglichkeiten der Parameterschätzung eingegangen werden.

•  A.C. Rencher und W.F. Christensen. Methods of Multivariate Analysis. John Wiley & Sons, Inc., 2012 (Chap. 13)
• J.F. Hair u. a. Multivariate Data Analysis. Pearson Education Limited, 2014 (Chap. 3)

Clusteranalyse

Die Clusteranalyse wird dazu verwendet um Daten, aus meist multivariaten Beobachtungen, anhand ähnlicher (Verhaltens-)Strukturen in sogenannte Cluster oder Gruppen zu ordnen. Das Ziel ist es optimale Gruppen für die Beobachtungen zu finden, sodass in jeder einzelnen Gruppe nur die Beobachtungen zusammengefasst werden, die eine ähnliche Struktur aufweisen, während die einzelnen Gruppen untereinander keine Ähnlichkeiten aufweisen. Um eine Gruppierung zu ermöglichen, gibt es verschiedene Algorithmen. Die einen betrachten alle Beobachtungspaare die auf Ähnlichkeit basieren. Dabei verwendet die Ähnlichkeitsanalyse eine sogenannte ”Measure of Distance”. Andere Algorithmen verwenden eine vorher festgelegte Clustermitte oder vergleichen die Variabilität der einzelnen Cluster mit- und untereinander. Das Anwendungsgebiet der Clusteranalyse ist vielfältig wie zum Beispiel Medizin, Soziologie, Kriminologie, Anthropologie, Archäologie, Geographie, Marktanalysen, Wirtschaftswissenschaften und Ingenieurwesen.

• A.C. Rencher und W.F. Christensen. Methods of Multivariate Analysis. John Wiley & Sons, Inc., 2012 (Chap. 15)
• J.F. Hair u. a. Multivariate Data Analysis. Pearson Education Limited, 2014 (Chap. 8)

k-Nearest-Neighbors

k-Nearest-Neighbors (k-NN) ist eine nicht-parametrische Klassifikationsmethode. Der Grundgedanke ist, einzelne Datenpunkte basierend auf der Klassenzugehörigkeit ihnen ähnlicher Datenpunkte - ihrer Nachbarn - zu klassifizieren. Neben der Definition von Entfernung spielt die Wahl des Parameters k, welcher die Größe der zu berücksichtigenden Nachbarschaft steuert, eine wichtige Rolle. In dieser Arbeit soll zunächst das Prinzip der Nächste-Nachbarn-Klassifikation und ihrer verschiedenen Ausprägungen vorgestellt werden, um darauf aufbauend die Wahl des Parameters k und der daraus folgenden Konsequenzen sowie die Evaluationsmöglichkeiten der resultierenden Klassifikation diskutieren zu können.

• W. Ertel und N.T. Black. Grundkurs K¨unstliche Intelligenz. Springer, 2016 (Kap. 8.3)
• C.M. Bishop u. a. Neural Networks for Pattern Recognition. Oxford University Press, 1995 (Kap. 2.5)

Autoregressive Prozesse

Eines der wichtigsten Modelle in der Zeitreihenanalyse ist der autoregressive Prozess (AR), bei dem Beobachtungen anhand von vergangenen Beobachtungen und einem Zufallsschock modelliert werden. Wenn die passende Modellordnung bekannt ist oder geschätzt wurde, also die Anzahl an zu berücksichtigenden vergangenen Beobachtungen, kann mit unterschiedlichen Methoden das Modell angepasst und zur Prognose genutzt werden. Interessant ist besonders die Eigenschaft der Stationarität des Prozesses. Einstiegsliteratur:

• M. Deistler und W. Scherrer. Modelle der Zeitreihenanalyse. Springer, 2018 (Kap. 5)
• K. Neusser. Zeitreihenanalyse in den Wirtschaftswissenschaften. Springer, 2009 (Kap. 2 + 5)

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.

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.

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.

Below you may find informationen about requirements for bachelor theses as well as a template for LaTeX. Your bachelor thesis should be 15 pages long.

For LaTeX beginners we recommend to use the university’s Overleaf cloud service ( https://www.luis.uni-hannover.de/de/services/speichersysteme/dateiservice/cloud-dienste/overleaf/ ). To start with, our template can easily be uploaded as a new project. Otherwise, proper installation of MiKTeX ( https://miktex.org/ ) and a LaTeX editor ( https://www.texstudio.org/ ) is required.

Entries for the bibliography file can be copied from Google Scholar (Cite -> BibTeX) or generated with e.g. https://www.doi2bib.org/ . In case of many references, a software for reference management (e.g. Citavi, https://www.luis.uni-hannover.de/de/services/betrieb-und-infrastruktur/software-lizenzen/software-katalog/produkte/citavi/ ) might be useful.

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