127 research outputs found
Functional quantization and metric entropy for Riemann-Liouville processes
We derive a high-resolution formula for the -quantization errors of
Riemann-Liouville processes and the sharp Kolmogorov entropy asymptotics for
related Sobolev balls. We describe a quantization procedure which leads to
asymptotically optimal functional quantizers. Regular variation of the
eigenvalues of the covariance operator plays a crucial role
Semiparametric posterior limits
We review the Bayesian theory of semiparametric inference following Bickel
and Kleijn (2012) and Kleijn and Knapik (2013). After an overview of efficiency
in parametric and semiparametric estimation problems, we consider the
Bernstein-von Mises theorem (see, e.g., Le Cam and Yang (1990)) and generalize
it to (LAN) regular and (LAE) irregular semiparametric estimation problems. We
formulate a version of the semiparametric Bernstein-von Mises theorem that does
not depend on least-favourable submodels, thus bypassing the most restrictive
condition in the presentation of Bickel and Kleijn (2012). The results are
applied to the (regular) estimation of the linear coefficient in partial linear
regression (with a Gaussian nuisance prior) and of the kernel bandwidth in a
model of normal location mixtures (with a Dirichlet nuisance prior), as well as
the (irregular) estimation of the boundary of the support of a monotone family
of densities (with a Gaussian nuisance prior).Comment: 47 pp., 1 figure, submitted for publication. arXiv admin note:
substantial text overlap with arXiv:1007.017
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Geometric Group Theory, Hyperbolic Dynamics and Symplectic Geometry
[no abstract available
Data depth and floating body
Little known relations of the renown concept of the halfspace depth for
multivariate data with notions from convex and affine geometry are discussed.
Halfspace depth may be regarded as a measure of symmetry for random vectors. As
such, the depth stands as a generalization of a measure of symmetry for convex
sets, well studied in geometry. Under a mild assumption, the upper level sets
of the halfspace depth coincide with the convex floating bodies used in the
definition of the affine surface area for convex bodies in Euclidean spaces.
These connections enable us to partially resolve some persistent open problems
regarding theoretical properties of the depth
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Geometric Group Theory, Hyperbolic Dynamics and Symplectic Geometry
The main theme of the workshop is the interaction between the speedily developing fields of mathematics mentioned in the title. One of the purposes of the workshop is to highlight new exciting developments which are happening right now on the borderline between hyperbolic dynamics, geometric group theory and symplectic geometry
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Dynamische Systeme (hybrid meeting)
This workshop continued a biannual series of workshops at Oberwolfach on
dynamical systems that started with a meeting organized by Moser and Zehnder in 1981.
Workshops in this series focus on new results and developments in
dynamical systems and related areas of mathematics, with symplectic geometry playing an important role in recent years in connection with Hamiltonian dynamics. In this year special emphasis was placed on various kinds of spectra (in contact geometry, in Riemannian geometry, in dynamical systems and in symplectic topology) and their applications to dynamics
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Dynamische Systeme
This workshop continued the biannual series at Oberwolfach on Dynamical Systems that started as the “Moser–Zehnder meeting” in 1981. The main themes of the workshop are the new results and developments in the area of dynamical systems, in particular in Hamiltonian systems and symplectic geometry. This year special emphasis where laid on symplectic methods with applications to dynamics. The workshop was dedicated to the memory of John Mather, Jean-Christophe Yoccoz and Krzysztof Wysocki
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