13,751 research outputs found
Extreme Value Theory Filtering Techniques for Outlier Detection
We introduce asymptotic parameter-free hypothesis tests based on extreme value theory to detect outlying observations in finite samples. Our tests have nontrivial power for detecting outliers for general forms of the parent distribution and can be implemented when this is unknown and needs to be estimated. Using these techniques this article also develops an algorithm to uncover outliers masked by the presence of influential observations
Testing the existence of clustering in the extreme values
This paper introduces an estimator for the extremal index as the ratio of the number of elements of two point processes defined by threshold sequences un, vn and a partition of the sequence in different blocks of the same size. The first point process is defined by the sequence of the block maxima that exceed un. This paper introduces a thinning of this point process, defined by a threshold vn with vn > un, and with the appealing property that under some mild conditions the ratio of the number of elements of both point processes is a consistent estimator of the extremal index. The method supports a hypothesis test for the extremal index, and hence for testing the existence of clustering in the extreme values. Other advantages are that it allows some freedom to choose un, and it is not very sensitive to the choice of the partition. Finally, the stylized facts found in financial returns (clustering, skewness, heavy tails) are tested via the extremal index, in this case for the DaX return
Palatini approach to bouncing cosmologies and DSR-like effects
It is shown that a quadratic gravitational Lagrangian in the Palatini
formulation is able to capture different aspects of quantum gravity
phenomenology in a single framework. In particular, in this theory field
excitations propagating with different energy-densities perceive different
background metrics, a fundamental characteristic of the DSR and Rainbow Gravity
approaches. This theory, however, avoids the so-called soccer ball problem.
Also, the resulting isotropic and anisotropic cosmologies are free from the big
bang singularity. This singularity avoidance occurs non-perturbatively and
shares some similitudes with the effective dynamics of loop quantum cosmology.Comment: 4 pages. Proceedings of Loops'11, Madrid. To appear in Journal of
Physics: Conference Series (JPCS
Cosmology in Palatini theories of gravity
We discuss recent results on the cosmology of extended theories of gravity
formulated in the Palatini approach, i.e., assuming that metric and connection
are independent fields. In particular, we focus on the attempts to explain the
cosmic speedup with f(R) theories and on models that avoid the big bang
singularity. The field equations for gravity Lagrangians of the form
f(g_{\mu\nu},{R^\alpha}_{\beta\mu\nu}) (including torsion) are explicitly
derived and discussed.Comment: 16 pages, no figures. Contribution to the Proceedings of Spanish
Relativity Meeting ERE2011, Madrid 29 August - 2 September 2011 . Plenary
tal
Re-examination of Polytropic Spheres in Palatini f(R) Gravity
We investigate spherically symmetric, static matter configurations with
polytropic equation of state for a class of f(R) models in Palatini formalism
and show that the surface singularities recently reported in the literature are
not physical in the case of Planck scale modified lagrangians. In such cases,
they are just an artifact of the idealized equation of state used. In fact, we
show that for the models f(R)=R\pm\lambda R^2, with \lambda on the order of the
Planck length squared, the presence of a single electron in the Universe would
be enough to cure all stellar singularities of this type. From our analysis it
also follows that the stellar structure derived from these lagrangians is
virtually undistinguishable from that corresponding to General Relativity. For
ultraviolet corrected models far from the Planck scale, however, the surface
singularities may indeed arise in the region of validity of the polytropic
equation of state. This fact can be used to place constraints on the parameters
of particular models
Introduction to Modified Gravity: From the Cosmic Speedup Problem to Quantum Gravity Phenomenology
These notes represent a summary of the introductory part of a course on
modified gravity delivered at several Spanish Universities (Granada, Valencia,
and Valladolid), at the University of Wisconsin-Milwaukee (WI, USA), and at the
Karl-Franzens Universitaet (Graz, Austria) during the period 2008-2011. We
begin with a discussion of the classical Newtonian framework and how special
relativity boosted the interest on new theories of gravity. Then we focus on
Nordstrom's scalar theories of gravity and their influence on Einstein's theory
of general relativity. We comment on the meaning of the Einstein equivalence
principle and its implications for the construction of alternative theories of
gravity. We present the cosmic speedup problem and how theories can be
constrained attending to their weak-field behavior. We conclude by showing that
Palatini f(R) and f(R,Q) theories can be used to address different aspects of
quantum gravity phenomenology and singularity problems.Comment: 34 pages, 2 figures. Chapter written for the book "Aspects of Today's
Cosmology", Edited by: Antonio Alfonso-Faus, InTech Publishing, Rijeka,
Croatia, (2011), ISBN 978-953-307-626-3. The properly formatted version (26
pages) can be freely downloaded from the publisher's websit
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