# Team > Prof. Dr. Melanie Birke

## Faculty of Mathematics, Physics and Computer Science

Working Group Mathematical Statistics

###### Research Team Teaching Theses Statistical Consulting Women's Representative DAV-Correspondent

Research

The working group works on topics in Nonparametric Statistics, Functional Data, Inverse Problems, Goodness-of-Fit Tests and Random Matrices. Details can be found under Priorities and Publications.

Team

Dipl. Math. M. Dorn

Teaching

Details on Teaching for the current and forthcomming semesters can be found at our Teaching page.

Bachelor and Master Theses

Possible topics for bachelor or master theses under my supervision come from nonparametric statistics, functional data or financial mathematics. To get an impression of the topics mentioned above please have a look at the Priorities of our working group. In your bachelor or master theses you can work purely theoretically on new statistical methods or also more practically by doing simulations or evaluate data sets with statistical methods.

If you are interested in writing your bachelor or master thesis under my supervision, just contact me. You can bring your own ideas for a topic or just ask me to give you a topic if you are uncertain what would be adequate.

Statistical Consulting

In complex experimental settings the evaluation of data often requires more sophisticated methods then known from classical statistics courses.

If you have questions regarding evaluation of your data you can contact me. In a first meeting, we will see, what is necessary in your situation and discuss the further proceeding.

Please note that we can only advice you in the kind of methods to use and interpretation of the results but **cannot** provide full evaluation of your data.

Women's Representative of the Mathematical Institute

As Deputy Women's Representative for the Faculty of Mathematics, Physics and Informatics I am the contact person for the academic staff especially of the Mathematical Institute in all questions regarding equal opportunities. Do not hesitate to contact me, if you have a question.

Information on centrally organized activities regarding equal opportunities like funding or mentoring programms can be found on the pages of the Equal Opportunities Department.

Relevant news for our faculty on forthcomming events are distributed via the E-Learning course "Gleichstellungsforum Fakultät 1".

DAV Correspondent

For starting the education as actuary a fundamental knowledge of probability theory and statistics is necessary. If you finished a mathematical program of study at University of Bayreuth and obtained a minimum of 30 ECTS in probability theory and statistics, you can contact me and ask for a confirmation that you already fulfill the requirements for starting the education without first attending a test. You definitely fulfill the requirements if you finished the following combination of courses

- Einführung in die Stochastik
- Einführung in die Statistik
- Vertiefung in Statistics, Probability Theory or Financial Mathematics
Seminar in Statistics, Probability Theory or Financial Mathematics

**or**a second Vertiefung in Statistics, Probability Theory or Financial Mathematics

Official Information on the education as actuary can be found at the pages of the DAV.

## Faculty of Mathematics, Physics and Computer Science

Working Group Mathematical Statistics

Nonparametric Statistics

Nonparametric statistics is the collection of all statistical methods which do not rely on a special parameterized statistical model. Nonparametric methods avoid errors caused by model misspecification.

The working group is especially interested in nonparametric methods for functional data, inverse problems and to construct goodness-of-fit tests for certain model assumptions

Functional Data

Functional Data became more and more important in the past years since with increasing capacities of computers, measurements over time can be observed over a finer and finer grid of time points. When using classical multivariate methods, the dimension gets to large to handle those data sets. That is, the observations are "closer" to a continuous time stochastic process than to a multivariate vector. It is necessary to develop new methods for analyzing this kind of data. A nowadays very prominent example of functional data are the Covid-19 incidences per country over a specific time period.

The working group is interested in estimators and the statistical inference for linear or nonparametric functional regression models as well as for parameters of functional data.

Inverse Problems

Inverse Problems occure in many kinds of data. To mention only a few settings images can be blurred by limitations of technical equipment. Similarly the result of a PCR is blurred by the fact, that not all particles of the same kind stop at the same point. This can be seen as a convolution of the original data with a density function. For estimating the truth, a deconvolution is necessary. To mention a last example, endogeneity of data where the error term is correlated with the regressor can be seen as inverse problem. Beyond these examples there are many others where inverse problems occur. What is the same in all settings, is that neglecting the inverse problem behind the data results in inconsistent estimators. Different estimators than in classical models are necessary.

The working group is interested in the statistical inference of those estimators resulting in tests or confidence bands for the true parameters.

Goodness-of-Fit Tests

Model assumptions are necessary to analyze statistical data. But what if the assumptions are not correct? This would result in wrong conclusions. Using Goodness-of-Fit Tests before analyzing the data with a statistical method based on a spezial model assumption one can make sure, that this assumption is valid.

Random Matrices

## Faculty of Mathematics, Physics and Computer Science

Working Group Mathematical Statistics

## Publications

**2013**

*Volgushev, Stanislav; Birke, Melanie; Dette, Holger; Neumeyer, Natalie*

** Significance testing in quantile regression**

*in *Electronic Journal of Statistics volume 7 (2013) . - page 105-145

doi:10.1214/12-EJS765 ...

*Birke, Melanie; Neumeyer, Natalie*

** Testing monotonicity of regression functions : an empirical process approach**

*in *Scandinavian Journal of Statistics volume 40 (2013) issue 3. - page 438-454

doi:10.1111/j.1467-9469.2012.00820.x ...

**2012**

*Birke, Melanie; Bissantz, Nicolai*

** Testing for symmetries in multivariate inverse problems**

*in *Journal of Multivariate Analysis volume 109 (2012) . - page 236-253

doi:10.1016/j.jmva.2012.03.008 ...

**2011**

*Birke, Melanie; Dette, Holger; Stahljans, Kristin*

** Testing symmetry of a nonparametric bivariate regression function**

*in *Journal of Nonparametric Statistics volume 23 (2011) issue 2. - page 547-565

doi:10.1080/10485252.2010.539687 ...

**2010**

*Birke, Melanie; Bissantz, Nicolai; Holzmann, Hajo*

** Confidence bands for inverse regression models**

*in *Inverse Problems volume 26 (2010) issue 11

doi:10.1088/0266-5611/26/11/115020 ...

**2009**

*Birke, Melanie; Pilz, Kay F.*

** Nonparametric Option Pricing with No-Arbitrage Constraints**

*in *Journal of Financial Econometrics volume 7 (2009) issue 2. - page 53-76

*Birke, Melanie; Dette, Holger*

** A note on some random orthogonal polynomials on a compact interval**

*in *Proceedings of the American Mathematical Society volume 137 (2009) issue 10. - page 3511-3522

doi:10.1090/S0002-9939-09-09933-X ...

*Birke, Melanie*

** Shape constrained kernel density estimation**

*in *Journal of Statistical Planning and Inference volume 139 (2009) issue 8. - page 2851-2862

doi:10.1016/j.jspi.2009.01.007 ...

**2008**

*Birke, Melanie*

** Central limit theorems for the integrated squared error of derivative estimators**

*in *Statistics & Probability Letters volume 78 (2008) issue 13. - page 1903-1913

doi:10.1016/j.spl.2008.01.058 ...

*Birke, Melanie; Dette, Holger*

** A note on estimating a smooth monotone regression by combining kernel and density estimates**

*in *Journal of Nonparametric Statistics volume 20 (2008) issue 8. - page 679-691

doi:10.1080/10485250802445399 ...

**2007**

*Birke, Melanie; Dette, Holger*

** Estimating a convex function in nonparametric regression**

*in *Scandinavian Journal of Statistics volume 34 (2007) issue 2. - page 384-404

doi:10.1111/j.1467-9469.2006.00534.x ...

*Birke, Melanie; Dette, Holger*

** Testing strict monotonicity in nonparametric regression**

*in *Mathematical Methods of Statistics volume 16 (2007) issue 2. - page 110-123

doi:10.3103/S1066530707020032 ...

## Faculty of Mathematics, Physics and Computer Science

Working Group Mathematical Statistics

**Prof. Dr. Melanie Birke**

Professor

Building: NW II, Room: 3.1.01.523

Phone: +49 (0)921 55-3289

E-mail: Melanie.Birke@uni-bayreuth.de

Homepage: Prof. Dr. M. Birke