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## Mathematisches Kolloquium

**Maître d’Enseignement, Dr. Christophe Ley**(Université libre de Bruxelles)

**"Skew-rotsymmetric distributions and related inferential procedures"**

Abstract: Directional data on unit spheres appear more and more frequently in diverse fields, the most modern being machine learning, bioinformatics and cosmology. Most classical distributions on the sphere, like the Fisher-von Mises-Langevin and the axial Watson distribution, assume that the data are rotationally symmetric about some location on the sphere. While this is an appealing assumption in some situations (e.g., when the earth rotation prevents us from distinguishing between two points of the same latitude), it often turns out to be an unrealistic assumption.

While many more flexible models have been proposed in the simpler circular case, the existence of such models for data on higher-dimensional spheres is rather scarce (except for some complicated mixture models).

To palliate this need, I will present in this talk a new class of flexible distributions, termed skew-rotsymmetric distributions. I will show their shape with some nice pictures, describe their properties (one very interesting property is that they keep some of the properties of rotationally symmetric distributions, for instance there is no need to calculate a normalizing constant, which is one of the heaviest tasks in spherical settings) as well as a simple generating mechanism, and establish optimal tests for rotational symmetry against skew-rotsymmetric alternatives. Of particular interest is the skew-rotsymmetric-FvML case, which suffers from a singular information matrix and hence is subject to the same criticism as the famous skew-normal distribution of Azzalini... to be continued! **10.11.2014, 11:15 - 12:45 Uhr**, (Ort noch unbekannt)

Kolloquiumsleiter: Prof. Dr. W.-D.Richter

**Prof. Dr. Arthur Pewsey**(Mathematics Department, University of Extremadura, Cáceres, Spain)

**"A Class of Circulas for Use with Toroidal Data"**

Abstract: We consider ‘circulas’; the circular analogues of copulas. More specifically, we concentrate on one particular class of bivariate circulas which is pre-existing but has not been studied in such explicit form or detail before. This class is appealing in many ways but does not necessarily result in especially attractive bivariate circular models when the marginals are not circular uniform. A major exception is an elegant bivariate wrapped Cauchy distribution proposed and developed by Kato & Pewsey (2013). We will consider properties of the circulas themselves, as well as those of distributions generated using circulas with marginals that are not circular uniform. Likelihood based inference for the latter distributions will be considered and applied in the modelling of wind directions at a Texan weather station and data on the pre-earthquake direction of steepest descent and post-earthquake direction of lateral ground movement before and after, respectively, an earthquake in Noshiro, Japan.

This is joint work with Chris Jones (OU, UK) and Shogo Kato (ISM, Japan). **16.10.2014, 11:15-12:45 Uhr, HS 421 (Ulmenstraße 69, Haus 3)**

Kolloquiumsleiter: Prof. Dr. W.-D.Richter

**Associate Professor Stefan Hoderlein**(Boston College (USA))

**"Nonparametric Identification of Endogenous and Heterogeneous Aggregate Demand Models: Complements, Bundles and the Market Level"**

Abstract: This paper studies nonparametric identification in market level demand models for differentiated products. We generalize common models by allowing for the distribution of heterogeneity parameters (random coefficients) to have a nonparametric distribution across the population and give conditions under which the density of the random coefficients is identified. We show that key identifying restrictions are provided by (i) a set of moment conditions generated by instrumental variables together with an inversion of aggregate demand in unobserved product characteristics; and (ii) an integral transform

(Radon transform) that maps the random coefficient density to the aggregate demand. This feature is shown to be common across a wide class of models, and we illustrate this by studying leading demand models. Our examples include demand models based on the multinomial choice (Berry, Levinsohn, Pakes, 1995), the choice of bundles of goods that can be substitutes or complements, and the choice of goods consumed in multiple units.**13.10.2014, 16:00 Uhr, HS 125 (Ulmenstr. 69, Haus 3)**

Kolloquiumsleiter: Prof. Dr. A. Meister

**M. Sc. Sebastian Kühnert**(Universität Siegen)

**"Parameterschätzung für Exponentially tempered Power Law - Verteilungen"****23.06.2014, 15:00 Uhr**, HS 125 (Ulmenstraße 69, Haus 3)

Kolloquiumsleiter: Prof. Dr. A. Meister

**Prof. Dr. Michael Joswig**(TU Berlin)

**"Infinite games, linear programs and tropical geometry"**

Abstract : Tropical geometry provides a framework for making available concepts from algebraic geometry and valuation theory in discrete mathematics. This way a number of maybe unexpected links appear. As an example we will discuss mean-payoff games, a certain class of infinite games, which are relevant from a computational complexity point of view. We will relate them to classical linear programming by means of tropical geometry.**15.01.2014, 15:00 Uhr, HS 125 (Ulmenstraße 69, Haus 3)**

Kolloquiumsleiter: Prof. Dr. A. Schürmann

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