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Prof. Dr. Götz Trenkler

The chair of Statistics and Econometrics works in the areas of **linear models, matrix algebra, non-parametrics, ** **point estimation, combination of economiy forecasts, admissibility and sports and statistics.**

The linear model is the most useful approach of portraying reality into a statistically manageable form. This basic model is needed in almost all areas of applications, in particular also in the area of economic research. The use of statistical methods to solve problems from the field of economics is summarised as 'econometrics'.

## Matrix Algebra

Matrices play a crucial role in statistics. Huge data sets are expressed in terms of matrices. Relationships between variables and their observations are analyzed with sophisticated matrix tools. Certain matrix types like range hermitian, normal or partial isometrics are of interest. Special attention is paid to oblique and orthogonal projectors and their properties.

## Non-Parametrics

In the framework of general statistics, also in the linear model,

certain assumptions about the distribution of random variables are often inevitable, mostly involving the Gaussian distribution. In non-parametric statistics, methods are derived which do not depend on these additional assumptions. This is of particular importance if no knowledge of the underlying distribution is available. Non-parametric methods, on the other hand, allow for sensible results even in theses cases.

## Point Estimation

In statistics, the problem to estimate unknown parameters of an existing distribution frequently occurs. For this purpose, both in univariate and in multivariate cases, there exists a number of estimation methods based on different assumptions and approaches. To name a few: maximum likelihood estimators, moment estimators and Jackknife estimators. Various characteristic properties, like unbiasedness, consistence or mean square error minimality, permit statements about the quality of the point estimators. Such reliable estimators have to be found and evaluated.

Frequently, an important economic parameter such as the gross national product is predicted by several different economic research institutes. As a general rule, these forecasts differ more or less strongly from one another, so that the question arises which of the forecasts should be preferred. Instead of choosing a single prediction, one can also try to combine the particular predictions to a general one. Since each of the separate forecasts is based on different information, there is justified hope that the combined forecast exceeds the separate ones.

## Admissibility

By the use of certain decision rules (estimators) to solve statistical problems, it is reasonable to claim that they are admissible within a class of decision rules. This means that they cannot be outperformed consistently by other rules from the same class. In linear regression models, linear estimators of parameter vectors play an important role. The analysis and description of admissible linear estimators is therefore a topic of modern research. Besides, the question of admissibility of non-linear estimators plays an important role in the literature, like methods of the Stein type.

## Sports and Statistics

Seminars focussing on "Sports and Statistics" are offered regularly. Several kinds of sports (for instance football, tennis, baseball, American football, basketball, figure skating) are analysed under different statistical points of view. In addition, various tournament systems are compared, or optimal strategies are presented. Further topics include doping, the advantage of playing at home and the world record development in sprinting.