L2L_2 boosting in kernel regression

In this paper, we investigate the theoretical and empirical properties of $L_2$ boosting with kernel regression estimates as weak learners. We show that each step of $L_2$ boosting reduces the bias of the estimate by two orders of magnitude, while it does not deteriorate the order of the variance. We illustrate the theoretical findings by some simulated examples. Also, we demonstrate that $L_2$ boosting is superior to the use of higher-order kernels, which is a well-known method of reducing the bias of the kernel estimate.Comment: Published in at http://dx.doi.org/10.3150/08-BEJ160 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Flexible generalized varying coefficient regression models

This paper studies a very flexible model that can be used widely to analyze the relation between a response and multiple covariates. The model is nonparametric, yet renders easy interpretation for the effects of the covariates. The model accommodates both continuous and discrete random variables for the response and covariates. It is quite flexible to cover the generalized varying coefficient models and the generalized additive models as special cases. Under a weak condition we give a general theorem that the problem of estimating the multivariate mean function is equivalent to that of estimating its univariate component functions. We discuss implications of the theorem for sieve and penalized least squares estimators, and then investigate the outcomes in full details for a kernel-type estimator. The kernel estimator is given as a solution of a system of nonlinear integral equations. We provide an iterative algorithm to solve the system of equations and discuss the theoretical properties of the estimator and the algorithm. Finally, we give simulation results.Comment: Published in at http://dx.doi.org/10.1214/12-AOS1026 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Tie-respecting bootstrap methods for estimating distributions of sets and functions of eigenvalues

Bootstrap methods are widely used for distribution estimation, although in some problems they are applicable only with difficulty. A case in point is that of estimating the distributions of eigenvalue estimators, or of functions of those estimators, when one or more of the true eigenvalues are tied. The $m$-out-of-$n$ bootstrap can be used to deal with problems of this general type, but it is very sensitive to the choice of $m$. In this paper we propose a new approach, where a tie diagnostic is used to determine the locations of ties, and parameter estimates are adjusted accordingly. Our tie diagnostic is governed by a probability level, $\beta$, which in principle is an analogue of $m$ in the $m$-out-of-$n$ bootstrap. However, the tie-respecting bootstrap (TRB) is remarkably robust against the choice of $\beta$. This makes the TRB significantly more attractive than the $m$-out-of-$n$ bootstrap, where the value of $m$ has substantial influence on the final result. The TRB can be used very generally; for example, to test hypotheses about, or construct confidence regions for, the proportion of variability explained by a set of principal components. It is suitable for both finite-dimensional data and functional data.Comment: Published in at http://dx.doi.org/10.3150/08-BEJ154 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Generalised additive dependency inflated models including aggregated covariates

Let us assume that X, Y and U are observed and that the conditional mean of U given X and Y can be expressed via an additive dependency of X, λ(X)Y and X + Y for some unspecified function . This structured regression model can be transferred to a hazard model or a density model when applied on some appropriate grid, and has important forecasting applications via structured marker dependent hazards models or structured density models including age-period-cohort relationships. The structured regression model is also important when the severity of the dependent variable has a complicated dependency on waiting times X, Y and the total waiting time X+Y . In case the conditional mean of U approximates a density, the regression model can be used to analyse the age-period-cohort model, also when exposure data are not available. In case the conditional mean of U approximates a marker dependent hazard, the regression model introduces new relevant age-period-cohort time scale interdependencies in understanding longevity. A direct use of the regression relationship introduced in this paper is the estimation of the severity of outstanding liabilities in non-life insurance companies. The technical approach taken is to use B-splines to capture the underlying one-dimensional unspecified functions. It is shown via finite sample simulation studies and an application for forecasting future asbestos related deaths in the UK that the B-spline approach works well in practice. Special consideration has been given to ensure identifiability of all models considered

Spatial Distribution of Metal Emissions in SNR 3C 397 Viewed with Chandra and XMM

We present X-ray equivalent width imaging of the supernova remnant (SNR) 3C 397 for Mg He\alpha, Si He\alpha, S He\alpha, and Fe K\alpha complex lines with the Chandra and XMM-Newton observations. The images reveal that the heavier the element is, the smaller the extent of the element distribution is. The Mg emission is evidently enhanced in the southeastern blow-out region, well along the radio boundary there, and appears to partially envelope the eastern Fe knot. Two bilateral hat-like Si line-emitting structures are along the northern and southern borders, roughly symmetric with respect to the southeast-northwest elongation axis. An S line-emitting shell is located just inner to the northern radio and IR shell, indicating of a layer of reversely shocked sulphur in the ejecta. A few enhanced Fe features are basically aligned along the diagonal of the rectangular shape of the SNR, which implicates an early asymmetric SN explosion.Comment: 4 pages, 4 figures, appears in Science China Physics, Mechanics & Astronomy, 2010, 53 (Suppl.1), 267-27

Generating Function for Particle-Number Probability Distribution in Directed Percolation

We derive a generic expression for the generating function (GF) of the particle-number probability distribution (PNPD) for a simple reaction diffusion model that belongs to the directed percolation universality class. Starting with a single particle on a lattice, we show that the GF of the PNPD can be written as an infinite series of cumulants taken at zero momentum. This series can be summed up into a complete form at the level of a mean-field approximation. Using the renormalization group techniques, we determine logarithmic corrections for the GF at the upper critical dimension. We also find the critical scaling form for the PNPD and check its universality numerically in one dimension. The critical scaling function is found to be universal up to two non-universal metric factors.Comment: (v1,2) 8 pages, 5 figures; one-loop calculation corrected in response to criticism received from Hans-Karl Janssen, (v3) content as publishe

Anisotropy of in-plane magnetization due to nodal gap structure in the vortex state

We examine the interplay between anisotropy of the in-plane magnetization and the nodal gap structure on the basis of the approximate analytic solution in the quasiclassical formalism. We show that a four-fold oscillation appears in the magnetization, and its amplitude changes sign at an intermediate field. The high-field oscillation originates from the anisotropy of the upper critical field, while the low-field behavior can be understood by the thermally activated quasiparticles near nodes depending on the applied field angles. The temperature dependence of the magnetization also shows a similar sign change. The anisotropy of the magnetization offers a possible measurement to identify the gap structure directly for a wide class of type II superconductors.Comment: 4 pages, 4 figure

Study of Low Energy Spin Rotons in the Fractional Quantum Hall Effect

Motivated by the discovery of extremely low energy collective modes in the fractional quantum Hall effect (Kang, Pinczuk {\em et al.}), with energies below the Zeeman energy, we study theoretically the spin reversed excitations for fractional quantum Hall states at $\nu=2/5$ and 3/7 and find qualitatively different behavior than for $\nu=1/3$. We find that a low-energy, charge-neutral "spin roton," associated with spin reversed excitations that involve a change in the composite-fermion Landau level index, has energy in reasonable agreement with experiment.Comment: Postscript figures included. Accepted in Phys. Rev. B (Rapid Communication

SPEAR Far Ultraviolet Spectral Images of the Cygnus Loop

We present far-ultraviolet (FUV) spectral images, measured at C IV 1550, He II 1640, Si IV+O IV] 1400, and O III] 1664, of the entire Cygnus Loop, observed with the Spectroscopy of Plasma Evolution from Astrophysical Radiation (SPEAR) instrument, also known as FIMS. The spatial distribution of FUV emission generally corresponds with a limb-brightened shell, and is similar to optical, radio and X-ray images. The features found in the present work include a ``carrot'', diffuse interior, and breakout features, which have not been seen in previous FUV studies. Shock velocities of 140-160 km/s is found from a line ratio of O IV] to O III], which is insensitive not only to resonance scattering but also to elemental abundance. The estimated velocity indicates that the fast shocks are widespread across the remnant. By comparing various line ratios with steady-state shock models, it is also shown that the resonance scattering is widespread.Comment: 13 pages, 3 figures, 1 table, accepted for publication in ApJ

Observation of thundercloud-related gamma rays and neutrons in Tibet

During the 2010 rainy season in Yangbajing (4300 m above sea level) in Tibet, China, a long-duration count enhancement associated with thunderclouds was detected by a solar-neutron telescope and neutron monitors installed at the Yangbajing Comic Ray Observatory. The event, lasting for ∼40  min, was observed on July 22, 2010. The solar-neutron telescope detected significant γ-ray signals with energies >40  MeV in the event. Such a prolonged high-energy event has never been observed in association with thunderclouds, clearly suggesting that electron acceleration lasts for 40 min in thunderclouds. In addition, Monte Carlo simulations showed that >10  MeV γ rays largely contribute to the neutron monitor signals, while >1  keV neutrons produced via a photonuclear reaction contribute relatively less to the signals. This result suggests that enhancements of neutron monitors during thunderstorms are not necessarily clear evidence for neutron production, as previously thought