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 f(T)f(T) theory

Recently, a new model obtained from generalizing teleparallel gravity, named $f(T)$ 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