Nonparametric inference in a model of recurrent events in the presence of a terminal event and independent right-censoring
Freitag, 1.2.08, 11:15-12:15, Raum 404, Eckerstr. 1
In clinical and epidemiological studies, subjects may experience recurrent events, such as myocardial infarctions. The recurrence of such serious events is often associated with a high risk of death with the consequence that subjects may die during the study. We focus on the gap times between successive events conditional on survival. For each recurrence, death and infarction are both of interest and are treated as competing risks. We consider the marginal cause-specific distribution function of the gap time between two successive infarctions and the cause-specific distribution function of the gap time between an infarction and death, both conditional on having survived the previous occurrences. We also consider the joint cause-specific distribution function of the successive gap times. We propose nonparametric estimators for these functions, in the presence of independent right-censoring. Strong consistency and weak convergence results are presented. We investigate the finite sample properties of the proposed estimators through simulations. Finally, the developed estimators are illustrated on a real dataset.
Freitag, 1.2.08, 17:00-18:00, Hörsaal II, Albertstr. 23b
Kähler Geometrie IX
Montag, 4.2.08, 16:15-17:15, Hörsaal II, Albertstr. 23b
Ballmann, W.: "Lectures on Kähler manifolds", Kap. 7
Navigation von und Interaktion mit humanoiden Robotern
Freitag, 8.2.08, 11:15-12:15, Raum 404, Eckerstr. 1
Eine grundlegende Motivation für die Forschung auf dem Gebiet humanoider Roboter liegt darin, Roboter zu entwickeln, die besser angepasst sind an die für Menschen geschaffenen Umgebungen. Dies erfordert, dass die Roboter mit Menschen interagieren können und trotz ihrer typischerweise eingeschränkten Ressourcen in der Lage sind, zuverlässig in ihren Umgebungen zu navigieren. In meinem Vortrag werde ich auf beide Aspekte eingehen.
\n\nIm ersten Teil meines Vortrages präsentiere ich probabilistische Techniken, welche es einem humanoiden Roboter erlauben, sich auf der Basis von Kamerabildern zuverlässig in seiner Umgebung zu lokalisieren. Neben den mathematischen Grundlagen werde ich auch Ergebnisse aus umfangreichen Experimenten mit echten humanoiden Robotern präsentieren.
\n\nIm zweiten Teil meines Vortrags stelle ich Verfahren zur natürlichen, intuitiven Interaktion eines Roboters mit Menschen vor. Diese Verfahren erlauben es dem Roboter robust die Positionen von Interaktionspartnern zu schätzen und typische Gesten, die Menschen ährend der Interaktion ausführen, zu erkennen und zu deuten.
Freitag, 8.2.08, 17:00-18:00, Hörsaal II, Albertstr. 23b
The prescribed Q-curvature problem on riemannian four-manifolds
Montag, 11.2.08, 16:15-17:15, Hörsaal II, Albertstr. 23b
Zweiphasen-Probleme für die Navier-Stokes-Gleichungen mit Oberflächenspannung
Dienstag, 12.2.08, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
On semi-parametric random censorship models
Freitag, 15.2.08, 11:15-12:15, Raum 404, Eckerstr. 1
In the random censorship model (RC) one observes data of the form\n(Z,δ), where Z = min(X,Y), X is independent of Y, and\nδ indicates whether X is censored (δ=0) or not\n(δ=1). Denote by m(x)=E(δ | Z=x) the\nregression function of the binary variable δ given Z=x and\nassume that m belongs to a parametric family with parameter space\nΘ ⊂ ℝk, i.e. m(x) = m(x,θ0) and θ0\n∊ Θ. RC together with such a binary model assumption defines\na semi-parametric random censorship model (SRC).
\n\nWe study a semi-parametric estimator of the distribution function\nF of X, which is based upon maximum likelihood estimation of\nθ0. Asymptotics of general semi-parametric integral\nestimators are discussed and compared to the corresponding\nasymptotic results of Kaplan-Meier integrals.
\n\nFinally, we study a diagnostic method to check whether the assumed\nparametric binary model is appropriate. These tests are based on\nsome asymptotic results of a marked empirical process and on a new\nresampling scheme of the bootstrap.
The derivative map for diffeomorphisms of disks
Freitag, 15.2.08, 17:00-18:00, Hörsaal II, Albertstr. 23b
The derivative map Diff(Dnrel dDn)-->ΩnO(n) is rationally null homotopic. I will show how this follows from the existence of rational Pontrjagin classes and explain how it is related to the stability theorem for Diff(Dn) and to Kervaire-Milnor's exotic spheres.\n