445 research outputs found
A new test procedure of independence in copula models via chi-square-divergence
We introduce a new test procedure of independence in the framework of
parametric copulas with unknown marginals. The method is based essentially on
the dual representation of -divergence on signed finite measures. The
asymptotic properties of the proposed estimate and the test statistic are
studied under the null and alternative hypotheses, with simple and standard
limit distributions both when the parameter is an interior point or not.Comment: 23 pages (2 figures). Submitted to publicatio
Functional limit laws for the increments of Kaplan-Meier product-limit processes and applications.
Approximations and two-sample tests based on P-P and Q-Q of the Kaplan-Meier estimators of lifetime distributions
No readable abstract
Strong Approximation of Empirical Copula Processes by Gaussian Processes
We provide the strong approximation of empirical copula processes by a
Gaussian process. In addition we establish a strong approximation of the
smoothed empirical copula processes and a law of iterated logarithm
Seismic evidence for a weak radial differential rotation in intermediate-mass core helium burning stars
The detection of mixed modes that are split by rotation in Kepler red giants
has made it possible to probe the internal rotation profiles of these stars,
which brings new constraints on the transport of angular momentum in stars.
Mosser et al. (2012) have measured the rotation rates in the central regions of
intermediate-mass core helium burning stars (secondary clump stars). Our aim
was to exploit& the rotational splittings of mixed modes to estimate the amount
of radial differential rotation in the interior of secondary clump stars using
Kepler data, in order to place constraints on angular momentum transport in
intermediate-mass stars. We selected a subsample of Kepler secondary clump
stars with mixed modes that are clearly rotationally split. By applying a
thorough statistical analysis, we showed that the splittings of both
gravity-dominated modes (trapped in central regions) and p-dominated modes
(trapped in the envelope) can be measured. We then used these splittings to
estimate the amount of differential rotation by using inversion techniques and
by applying a simplified approach based on asymptotic theory (Goupil et al.
2013). We obtained evidence for a weak radial differential rotation for six of
the seven targets that were selected, with the central regions rotating
to times faster than the envelope. The last target was
found to be consistent with a solid-body rotation. This demonstrates that an
efficient redistribution of angular momentum occurs after the end of the main
sequence in the interior of intermediate-mass stars, either during the
short-lived subgiant phase, or once He-burning has started in the core. In
either case, this should bring constraints on the angular momentum transport
mechanisms that are at work.Comment: 16 pages, 8 figures, accepted in A&
Open issues in probing interiors of solar-like oscillating main sequence stars: 2. Diversity in the HR diagram
We review some major open issues in the current modelling of low and
intermediate mass, main sequence stars based on seismological studies. The
solar case was discussed in a companion paper, here several issues specific to
other stars than the Sun are illustrated with a few stars observed with CoRoT
and expectations from Kepler data.Comment: GONG 2010 - SoHO 24, A new era of seismology of the Sun and
solar-like stars, To be published in the Journal of Physics: Conference
Series (JPCS
Estimating stellar mean density through seismic inversions
Determining the mass of stars is crucial both to improving stellar evolution
theory and to characterising exoplanetary systems. Asteroseismology offers a
promising way to estimate stellar mean density. When combined with accurate
radii determinations, such as is expected from GAIA, this yields accurate
stellar masses. The main difficulty is finding the best way to extract the mean
density from a set of observed frequencies.
We seek to establish a new method for estimating stellar mean density, which
combines the simplicity of a scaling law while providing the accuracy of an
inversion technique.
We provide a framework in which to construct and evaluate kernel-based linear
inversions which yield directly the mean density of a star. We then describe
three different inversion techniques (SOLA and two scaling laws) and apply them
to the sun, several test cases and three stars.
The SOLA approach and the scaling law based on the surface correcting
technique described by Kjeldsen et al. (2008) yield comparable results which
can reach an accuracy of 0.5 % and are better than scaling the large frequency
separation. The reason for this is that the averaging kernels from the two
first methods are comparable in quality and are better than what is obtained
with the large frequency separation. It is also shown that scaling the large
frequency separation is more sensitive to near-surface effects, but is much
less affected by an incorrect mode identification. As a result, one can
identify pulsation modes by looking for an l and n assignment which provides
the best agreement between the results from the large frequency separation and
those from one of the two other methods. Non-linear effects are also discussed
as is the effects of mixed modes. In particular, it is shown that mixed modes
bring little improvement as a result of their poorly adapted kernels.Comment: Accepted for publication in A&A, 20 pages, 19 figure
A transmission problem across a fractal self-similar interface
We consider a transmission problem in which the interior domain has
infinitely ramified structures. Transmission between the interior and exterior
domains occurs only at the fractal component of the interface between the
interior and exterior domains. We also consider the sequence of the
transmission problems in which the interior domain is obtained by stopping the
self-similar construction after a finite number of steps; the transmission
condition is then posed on a prefractal approximation of the fractal interface.
We prove the convergence in the sense of Mosco of the energy forms associated
with these problems to the energy form of the limit problem. In particular,
this implies the convergence of the solutions of the approximated problems to
the solution of the problem with fractal interface. The proof relies in
particular on an extension property. Emphasis is put on the geometry of the
ramified domain. The convergence result is obtained when the fractal interface
has no self-contact, and in a particular geometry with self-contacts, for which
an extension result is proved
Approximations and two-sample tests based on P-P and Q-Q plots of the Kaplan-Meier estimators of lifetime distributions.
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