695 research outputs found
An overview of the goodness-of-fit test problem for copulas
We review the main "omnibus procedures" for goodness-of-fit testing for
copulas: tests based on the empirical copula process, on probability integral
transformations, on Kendall's dependence function, etc, and some corresponding
reductions of dimension techniques. The problems of finding asymptotic
distribution-free test statistics and the calculation of reliable p-values are
discussed. Some particular cases, like convenient tests for time-dependent
copulas, for Archimedean or extreme-value copulas, etc, are dealt with.
Finally, the practical performances of the proposed approaches are briefly
summarized
Wigner Measure Propagation and Conical Singularity for General Initial Data
We study the evolution of Wigner measures of a family of solutions of a
Schr\"odinger equation with a scalar potential displaying a conical
singularity. Under a genericity assumption, classical trajectories exist and
are unique, thus the question of the propagation of Wigner measures along these
trajectories becomes relevant. We prove the propagation for general initial
data.Comment: 24 pages, 1 figur
Single-index copulae
We introduce so-called "single-index copulae". They are semi-parametric
conditional copulae whose parameter is an unknown "link" function of a
univariate index only. We provide estimates of this link function and of the
finite dimensional unknown parameter. The asymptotic properties of the latter
estimates are stated. Thanks to some properties of conditional Kendall's tau,
we illustrate our technical conditions with several usual copula families.Comment: Revised version: correction of Assumption 3 and some minor induced
modification
Defect measures on graded lie groups
In this article, we define a generalisation of microlocal defect measures
(also known as H-measures) to the setting of graded nilpotent Lie groups. This
requires to develop the notions of homogeneous symbols and classical
pseudo-differential calculus adapted to this setting and defined via the
representations of the groups. Our method relies on the study of the C
*-algebra of 0-homogeneous symbols. Then, we compute microlocal defect measures
for concentrating and oscillating sequences, which also requires to investigate
the notion of oscillating sequences in graded Lie groups. Finally, we discuss
compacity compactness approaches in the context of graded nilpotent Lie groups
On kernel-based estimation of conditional Kendall's tau: finite-distance bounds and asymptotic behavior
We study nonparametric estimators of conditional Kendall's tau, a measure of
concordance between two random variables given some covariates. We prove
non-asymptotic bounds with explicit constants, that hold with high
probabilities. We provide "direct proofs" of the consistency and the asymptotic
law of conditional Kendall's tau. A simulation study evaluates the numerical
performance of such nonparametric estimators.Comment: 29 pages, 4 figures. arXiv admin note: text overlap with
arXiv:1802.0761
Analysis of the Energy Decay of a Degenerated Thermoelasticity System
In this paper, we study a system of thermoelasticity with a degenerated
second order operator in the Heat equation. We analyze the evolution of the
energy density of a family of solutions. We consider two cases: when the set of
points where the ellipticity of the Heat operator fails is included in a
hypersurface and when it is an open set. In the first case and under special
assumptions, we prove that the evolution of the energy density is the one of a
damped wave equation: propagation along the rays of geometric optic and damping
according to a microlocal process. In the second case, we show that the energy
density propagates along rays which are distortions of the rays of geometric
optic.Comment: 28 page
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