185,863 research outputs found
Single-index quantile regression
This is the post-print version of the final paper published in Journal of Multivariate Analysis. The published article is available from the link below. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. Copyright @ 2010 Elsevier B.V.Nonparametric quantile regression with multivariate covariates is a difficult estimation problem due to the “curse of dimensionality”. To reduce the dimensionality while still retaining the flexibility of a nonparametric model, we propose modeling the conditional quantile by a single-index function View the MathML sourceg0(xTγ0), where a univariate link function g0(⋅)g0(⋅) is applied to a linear combination of covariates View the MathML sourcexTγ0, often called the single-index. We introduce a practical algorithm where the unknown link function g0(⋅)g0(⋅) is estimated by local linear quantile regression and the parametric index is estimated through linear quantile regression. Large sample properties of estimators are studied, which facilitate further inference. Both the modeling and estimation approaches are demonstrated by simulation studies and real data applications
Black hole remnant in asymptotic Anti-de Sitter space
It is known that a solution of remnant were suggested for black hole ground
state after surface gravity is corrected by loop quantum effect. On the other
hand, a Schwarzschild black hole in asymptotic Anti-de Sitter space would
tunnel into the thermal soliton solution known as the Hawking-Page phase
transition. In this letter, we investigate the low temperature phase of
three-dimensional BTZ black hole and four-dimensional AdS Schwarzschild black
hole. We find that the thermal soliton is energetically favored than the
remnant solution at low temperature in three dimensions, while Planck-size
remnant is still possible in four dimensions. Though the BTZ remnant seems
energetically disfavored, we argue that it is still possible to be found in the
overcooled phase if strings were present and its implication is discussed.Comment: 13 pages, 5 figures, submitted versio
The dynamical behavior of theory
Recently, a new model obtained from generalizing teleparallel gravity, named
theory, is proposed to explain the present cosmic accelerating expansion
with no need of dark energy. In this paper, we analyze the dynamical property
of this theory. For a concrete power law model, we obtain that the dynamical
system has a stable de Sitter phase along with an unstable radiation dominated
phase and an unstable matter dominated one. We show that the Universe can
evolve from a radiation dominated era to a matter dominated one, and finally
enter an exponential expansion phase.Comment: 10 pages, 1 figure; accepted by PL
Observational constraints on theory
The theory, which is an extension of teleparallel, or torsion scalar
, gravity, is recently proposed to explain the present cosmic accelerating
expansion with no need of dark energy. In this Letter, we first perform the
statefinder analysis and diagnostic to two concrete models,
i.e., and , and find that
a crossing of phantom divide line is impossible for both models. This is
contrary to an existing result where a crossing is claimed for the second
model. We, then, study the constraints on them from the latest Union 2 Type Ia
Supernova (Sne Ia) set, the baryonic acoustic oscillation (BAO), and the cosmic
microwave background (CMB) radiation. Our results show that at the 95%
confidence level ,
for Model 1 and ,
for Model 2. A comparison of these two models with
the CDM by the (dof: degree of freedom) criterion
indicates that CDM is still favored by observations. We also study the
evolution of the equation of state for the effective dark energy in the theory
and find that Sne Ia favors a phantom-like dark energy, while Sne Ia + BAO +
CMB prefers a quintessence-like one.Comment: 15 pages, 5 figures; statefinder diagnostic added, Om(z) analysis
added; references added; accepted by PL
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