68,462 research outputs found
Gravitational Lensing Statistics as a Probe of Dark Energy
By using the comoving distance, we derive an analytic expression for the
optical depth of gravitational lensing, which depends on the redshift to the
source and the cosmological model characterized by the cosmic mass density
parameter , the dark energy density parameter and its
equation of state . It is shown that, the larger the
dark energy density is and the more negative its pressure is, the higher the
gravitational lensing probability is. This fact can provide an independent
constraint for dark energy.Comment: 9 pages, 2 figure
Robust variable selection for nonlinear models with diverging number of parameters
We focus on the problem of simultaneous variable selection and estimation for nonlinear models based on modal regression (MR), when the number of coefficients diverges with sample size. With appropriate selection of the tuning parameters, the resulting estimator is shown to be consistent and to enjoy the oracle properties
Gravitational lensing statistical properties in general FRW cosmologies with dark energy component(s): analytic results
Various astronomical observations have been consistently making a strong case
for the existence of a component of dark energy with negative pressure in the
universe. It is now necessary to take the dark energy component(s) into account
in gravitational lensing statistics and other cosmological tests. By using the
comoving distance we derive analytic but simple expressions for the optical
depth of multiple image, the expected value of image separation and the
probability distribution of image separation caused by an assemble of singular
isothermal spheres in general FRW cosmological models with dark energy
component(s). We also present the kinematical and dynamical properties of these
kinds of cosmological models and calculate the age of the universe and the
distance measures, which are often used in classical cosmological tests. In
some cases we are able to give formulae that are simpler than those found
elsewhere in the literature, which could make the cosmological tests for dark
energy component(s) more convenient.Comment: 14 pages, no figure, Latex fil
Accelerating universe from gravitational leakage into extra dimensions: confrontation with SNeIa
There is mounting observational evidence that the expansion of our universe
is undergoing an acceleration. A dark energy component has usually been invoked
as the most feasible mechanism for the acceleration. However, it is desirable
to explore alternative possibilities motivated by particle physics before
adopting such an untested entity. In this work, we focus our attention on an
acceleration mechanism: one arising from gravitational leakage into extra
dimensions. We confront this scenario with high- type Ia supernovae compiled
by Tonry et al. (2003) and recent measurements of the X-ray gas mass fractions
in clusters of galaxies published by Allen et al. (2002,2003). A combination of
the two databases gives at a 99% confidence level that
, , and
, indicating a closed universe. We then
constrain the model using the test of the turnaround redshift, , at
which the universe switches from deceleration to acceleration. We show that, in
order to explain that acceleration happened earlier than within
the framework of gravitational leakage into extra dimensions, a low matter
density, , or a closed universe is necessary.Comment: 16 pages, 4 figures, accepted for publication in Ap
Robust variable selection in partially varying coefficient single-index model
By combining basis function approximations and smoothly clipped absolute deviation (SCAD) penalty, this paper proposes a robust variable selection procedure for a partially varying coefficient single-index model based on modal regression. The proposed procedure simultaneously selects significant variables in the parametric components and the nonparametric components. With appropriate selection of the tuning parameters, we establish the theoretical properties of our procedure, including consistency in variable selection and the oracle property in estimation. Furthermore, we also discuss the bandwidth selection and propose a modified expectation-maximization (EM)-type algorithm for the proposed estimation procedure. The finite sample properties of the proposed estimators are illustrated by some simulation examples.The research of Zhu is partially supported by National Natural Science Foundation of China (NNSFC) under Grants 71171075, 71221001 and 71031004. The research of Yu is supported by NNSFC under Grant 11261048
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