148,386 research outputs found
Bernstein von Mises Theorems for Gaussian Regression with increasing number of regressors
This paper brings a contribution to the Bayesian theory of nonparametric and
semiparametric estimation. We are interested in the asymptotic normality of the
posterior distribution in Gaussian linear regression models when the number of
regressors increases with the sample size. Two kinds of Bernstein-von Mises
Theorems are obtained in this framework: nonparametric theorems for the
parameter itself, and semiparametric theorems for functionals of the parameter.
We apply them to the Gaussian sequence model and to the regression of functions
in Sobolev and classes, in which we get the minimax convergence
rates. Adaptivity is reached for the Bayesian estimators of functionals in our
applications
Poisson bracket, deformed bracket and gauge group actions in Kontsevich deformation quantization
We express the difference between Poisson bracket and deformed bracket for
Kontsevich deformation quantization on any Poisson manifold by means of second
derivative of the formality quasi-isomorphism. The counterpart on star products
of the action of formal diffeomorphisms on Poisson formal bivector fields is
also investigated.Comment: 11 pages, one xypic figure. Minor changes on section I
A dichotomy characterizing analytic digraphs of uncountable Borel chromatic number in any dimension
We study the extension of the Kechris-Solecki-Todorcevic dichotomy on
analytic graphs to dimensions higher than 2. We prove that the extension is
possible in any dimension, finite or infinite. The original proof works in the
case of the finite dimension. We first prove that the natural extension does
not work in the case of the infinite dimension, for the notion of continuous
homomorphism used in the original theorem. Then we solve the problem in the
case of the infinite dimension. Finally, we prove that the natural extension
works in the case of the infinite dimension, but for the notion of
Baire-measurable homomorphism
Oblique repulsion in the nonnegative quadrant
We consider an electrostatic attractive-repulsive differential system in the
nonnegative quadrant. Under some condition on the constants there exists a
unique global solution. The main difficulty is to prove uniqueness when
starting at the corner of the quadrant
Codimension one holomorphic foliations on : problems in complex geometry
After a short review on foliations, we prove that a codimension 1 holomorphic
foliation on with simple singularities is given by a
closed rational 1-form. The proof uses Hironaka-Matsumura prolongation theorem
of formal objects
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