80,183 research outputs found
Tails of correlation mixtures of elliptical copulas
Correlation mixtures of elliptical copulas arise when the correlation
parameter is driven itself by a latent random process. For such copulas, both
penultimate and asymptotic tail dependence are much larger than for ordinary
elliptical copulas with the same unconditional correlation. Furthermore, for
Gaussian and Student t-copulas, tail dependence at sub-asymptotic levels is
generally larger than in the limit, which can have serious consequences for
estimation and evaluation of extreme risk. Finally, although correlation
mixtures of Gaussian copulas inherit the property of asymptotic independence,
at the same time they fall in the newly defined category of near asymptotic
dependence. The consequences of these findings for modeling are assessed by
means of a simulation study and a case study involving financial time series.Comment: 21 pages, 3 figure
SPADES and mixture models
This paper studies sparse density estimation via penalization
(SPADES). We focus on estimation in high-dimensional mixture models and
nonparametric adaptive density estimation. We show, respectively, that SPADES
can recover, with high probability, the unknown components of a mixture of
probability densities and that it yields minimax adaptive density estimates.
These results are based on a general sparsity oracle inequality that the SPADES
estimates satisfy. We offer a data driven method for the choice of the tuning
parameter used in the construction of SPADES. The method uses the generalized
bisection method first introduced in \citebb09. The suggested procedure
bypasses the need for a grid search and offers substantial computational
savings. We complement our theoretical results with a simulation study that
employs this method for approximations of one and two-dimensional densities
with mixtures. The numerical results strongly support our theoretical findings.Comment: Published in at http://dx.doi.org/10.1214/09-AOS790 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
A data driven equivariant approach to constrained Gaussian mixture modeling
Maximum likelihood estimation of Gaussian mixture models with different
class-specific covariance matrices is known to be problematic. This is due to
the unboundedness of the likelihood, together with the presence of spurious
maximizers. Existing methods to bypass this obstacle are based on the fact that
unboundedness is avoided if the eigenvalues of the covariance matrices are
bounded away from zero. This can be done imposing some constraints on the
covariance matrices, i.e. by incorporating a priori information on the
covariance structure of the mixture components. The present work introduces a
constrained equivariant approach, where the class conditional covariance
matrices are shrunk towards a pre-specified matrix Psi. Data-driven choices of
the matrix Psi, when a priori information is not available, and the optimal
amount of shrinkage are investigated. The effectiveness of the proposal is
evaluated on the basis of a simulation study and an empirical example
Transport properties for liquid silicon-oxygen-iron mixtures at Earth's core conditions
We report on the thermal and electrical conductivities of two liquid
silicon-oxygen-iron mixtures (FeSiO and
FeSiO), representative of the composition of the
Earth's outer core at the relevant pressure-temperature conditions, obtained
from density functional theory calculations with the Kubo-Greenwood
formulation. We find thermal conductivities =100 (160) W m K,
and electrical conductivities
m at the top (bottom) of the outer core. These new values are between 2
and 3 times higher than previous estimates, and have profound implications for
our understanding of the Earth's thermal history and the functioning of the
Earth's magnetic field, including rapid cooling rate for the whole core or high
level of radiogenic elements in the core. We also show results for a number of
structural and dynamic properties of the mixtures, including the partial radial
distribution functions, mean square displacements, viscosities and speeds of
sound.Comment: 16 pages, 12 figure
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