Institut für Mathematik - Mathematisches Kolloquium

• Prof. Dr. Uwe Leck (U Wisconsin, Superior, USA)

"Über eine Vermutung von Roberts für den Vereinigungsabschluss uniformer Mengenfamilien"
Abstract : Im Kolloquium vor drei Jahren hatte ich über die MUC-Vermutung von Ian Roberts aus dem Jahr 1999 berichtet. Diese bezieht sich auf das folgende Problem: Für gegebene m,k finde man m k-Mengen, so dass die Kardinalität des von ihnen generierten Vereinigungsabschlusses minimiert wird. Die Vermutung besagt, dass es bestmöglich ist, die ersten m k-Mengen bezüglich einer linearen Ordnung aller k-Mengen über den natürlichen Zahlen zu wählen, die global antilexikographisch und lokal lexikographisch ist. Im Vortrag werden einige neue Ergebnisse zur MUC-Vermutung vorgestellt, insbesondere eine gewichtete Version für k=2 und deren Beweis, sowie neue Resultate für cross-unions.
30.05.2012, 15:00 Uhr, Ulmenstraße 69, Haus 3, HS 125
Kolloquiumsleiter: Prof. Dr. H.-D. Gronau

• Dr. Bogdan Ichim (Uni Osnabrück / Bukarest)

"Introduction to Normaliz"
Abstract: We introduce Normaliz, a program for the computation of Hilbert bases and Hilbert series of rational cones. It may also be used for solving diophantine linear systems of inequalities, equations and congruences.
We present some of the new features of the program, as well as some recent achievements.
09.05.2012, 15:00 Uhr, Ulmenstraße 69, Haus 3, HS 125
Kolloquiumsleiter: Prof. Dr. A. Schürmann

• Associate Professor Aurore Delaigle (University of Melbourne, Australien)

"Nonparametric Regression from Group Testing Data"
Abstract : To reduce cost and increase speed of large screening studies, data are often pooled in groups. In these cases, instead of carrying out a test (say a blood test) on all individuals in the study to see if they if they are infected or not, one only tests the pooled blood of all individuals in each group. We consider this problem when a covariate is also observed, and one is interested in estimating the conditional probability of contamination. We show how to  estimate this conditional probability using a simple nonparametric estimator. We illustrate the procedure on data from the NHANES study.
04.05.2012, 13:30-14:30 Uhr, Ulmenstraße 69, Haus 3, Raum 421
Kolloquiumsleiter: Prof. Dr. A. Meister

• Prof. Dr. Enno Mammen (Universität Mannheim)

"Testing Parametric Mean Specifications in Semiparametric GARCH-in-Mean Models"
Abstract
12.04.2012, 17:15 Uhr, Ulmenstraße 69, Haus 3, HS 326/327
Kolloquiumsleiter: Prof. Dr. H. Milbrodt

• Prof. Dr. Bernhard Burgeth (Universität des Saarlandes)

"Mathematical Morphology for Matrix Fields"
24.02.2012, 11:00 Uhr, Ulmenstraße 69, Haus 3, HS 125
Kolloquiumsleiter: Prof. Dr. K. Engel

• Prof. Dr. Milan Stehlík (Johannes Kepler Universität Linz)

"Methods for deriving exact distributions"
Abstract: Many statistical problems defined in applications end up with a complicated hypothesis testing. Such statistics may have complicated, unknown or untractable exact, even asymptotic distributions. For example, consider asymptotical behavior of likelihood ratio test statistic at singular points of hypothesis (see Drton (2009)). However, many times, exact distribution of the statistics may be derived. We will discuss some methods of derivation of exact or nearly exact test. For instance, we will derive exact likelihood ratio test of simple hypothesis for scale parameter in the case of Type I and progressively Type II censored Weibull samples (see Balakrishnan and Stehlík (2008)) and procedure for simulation of quantiles for homogeneity tests in the case of Weibull with subpopulation model (see Stehlík and Wagner (2011)). We will illustrate such a tests to be comparable with others, and in some setups even superior to frequently used tests for exponential homogeneity which are based on the EM algorithm (like the MLRT, the ADDS test, and the D-tests). One important example of such superiority is the case of lower contamination. In reliability engineering, the inference problem for the complete samples and large data sets are commonly rare events. Typically, missing data are present and censoring has been applied. Moreover, samples are frequently small because of many reasons (e.g. expensive observations or rare event structure of the failure process). During the talk we will discuss recent results on the exact likelihood ratio tests of scale and homogeneity hypotheses when samples are from exponential, Erlang, gamma (see Stehlík (2003)), Weibull (see Stehlík (2006)) and generalized gamma distributions (see Stehlík (2008)). The asymptotical tests are typically oversized and thus inappropriate for small samples. We will mention the reliability prediction when some data is missing or is censored. The reliability prediction when some data is missing plays a major role in many reliability programs (e.g. for a variety of reasons over 90% of the data in the Reliability Analysis Center does not have the individual failure times recorded, see Coit and Jin (2000)). We will provide also recent results for exact testing with missing data (see Stehlík (2008)). The real data examples and various applications (see Stehlík and Ososkov (2003)) will illustrate the topics discussed.
06.02.2012, 11:00 Uhr, Ulmenstraße 69, Haus 3, HS 326/327
Kolloquiumsleiter: Prof. Dr. W.-D. Richter

• Prof. Dr. Volkmar Liebscher (Ernst-Moritz-Arndt-Universität Greifswald)

"Komplexitätsbestrafte Regression in der Bild- und Signalanalyse"
Abstract : Verschiedene Beispiele von Zeitreihen-artigen Daten aus den Lebenswissenschaften, aber auch aus der Bildanalyse, fordern uns zu einer Partitionierung der Daten in homogene Bereiche auf. In dem Vortrag werden verschiedene Optimierungsprobleme präsentiert, die solche Partitionierungsprobleme mathematisch lösbar machen. Allen gemeinsam sind zwei Terme in dem zu minimierenden Funktional: einer beschreibt die Komplexität des partitionierten Signales und einer die Treue zu den Ausgangsdaten. Da der Komplexitätsterm im wesentlichen ganzzahlig ist, benötigt ein Optimierungsalgorithmus auch wesentlich Methoden aus der Diskreten Optimierung, speziell Dynamische Programmierung. Neben der algorithmischen Lösung wird auch auf Beziehungen zu Approximationsräumen und statistischer Konsistenz der Verfahren eingegangen.    
25.01.2012, 15:00 Uhr, Ulmenstraße 69, Haus 3, HS 125
Kolloquiumsleiter: Prof. Dr. K. Engel

• Dipl.-Math. Johanna Kappus (Humboldt-Universität zu Berlin)

"Nonparametric estimation for pure jump Levy processes with a view towards nonparametric density deconvolution with unknown distribution of the noise"
Abstract : Given discrete, equidistant observations of a pure jump Levy process, the goal is to estimate a linear functional of the underlying jump measure.
We construct spectral cuto ff and general kernel estimators and derive upper bounds on the corresponding risk. The main focus of this talk lies on the problem of adaptive estimation via model selection. It is interesting to note that nonparametric estimation for pure jump Levy processes is intimately connected to the problem of nonparametric density deconvolution with unknown distribution of the noise, which is still of independent interest. For this reason, we study both concepts in parallel and develop a new approach to model selection with unknown variance.           
23.01.2012, 15:00-17:00 Uhr, Ulmenstraße 69, Haus 3, HS 326/327
Kolloquiumsleiter: Prof. Dr. A. Meister

• Prof. Stefan Hoderlein (Boston College, USA)

"Semiparametric Estimation of Random Coefficients in Structural Economic Models"
Abstract : In structural economic models, individuals are usually characterized as solving a decision problem that is governed by a finite set of parameters. This paper discusses the nonparametric estimation of the density of these parameters if they are allowed to vary continuously across the population. We establish that the problem of recovering the density of random parameters falls into the class of non-linear inverse problem. This framework helps us to answer the question whether there exist densities that satisfy this relationship. It also allows us to characterize the identified set of such densities, to obtain
conditions for point identification, and to establish that point identification is weak. Given this insight, we propose a consistent nonparametric estimator, and derive its asymptotic distribution. Our general framework allows us to deal with unobservable nuisance variables, e.g., measurement error, but also covers the case when there are no such nuisance variables. Finally, Monte Carlo experiments for several structural models are provided which illustrate the performance of our estimation procedure.
19.01.2012, 15:00 - 17:00 Uhr, Ulmenstraße 69, Haus 3, Seminarraum 421
Kolloquiumsleiter: Prof. Dr. A. Meister

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