Iterated smoothed bootstrap confidence intervals for population quantiles

This paper investigates the effects of smoothed bootstrap iterations on coverage probabilities of smoothed bootstrap and bootstrap-t confidence intervals for population quantiles, and establishes the optimal kernel bandwidths at various stages of the smoothing procedures. The conventional smoothed bootstrap and bootstrap-t methods have been known to yield one-sided coverage errors of orders O(n^{-1/2}) and o(n^{-2/3}), respectively, for intervals based on the sample quantile of a random sample of size n. We sharpen the latter result to O(n^{-5/6}) with proper choices of bandwidths at the bootstrapping and Studentization steps. We show further that calibration of the nominal coverage level by means of the iterated bootstrap succeeds in reducing the coverage error of the smoothed bootstrap percentile interval to the order O(n^{-2/3}) and that of the smoothed bootstrap-t interval to O(n^{-58/57}), provided that bandwidths are selected of appropriate orders. Simulation results confirm our asymptotic findings, suggesting that the iterated smoothed bootstrap-t method yields the most accurate coverage. On the other hand, the iterated smoothed bootstrap percentile method interval has the advantage of being shorter and more stable than the bootstrap-t intervals.Comment: Published at http://dx.doi.org/10.1214/009053604000000878 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Note on: "Domain wall universe in the Einstein--Born--Infeld theory" Phys. Lett. B 679 (2009) 160

The interaction between bulk and dynamic domain wall in the presence of a linear / non-linear electromagnetism make energy density, tension and pressure on the wall all variables, depending on the wall position. In [1] this fact seems to be ignored.Comment: 4 pages, 1 figur

Instanton solutions mediating tunneling between the degenerate vacua in curved space

We investigate the instanton solution between the degenerate vacua in curved space. We show that there exist $O(4)$-symmetric solutions not only in de Sitter but also in both flat and anti-de Sitter space. The geometry of the new type of solutions is finite and preserves the $Z_2$ symmetry. The nontrivial solution corresponding to the tunneling is possible only if gravity is taken into account. The numerical solutions as well as the analytic computations using the thin-wall approximation are presented. We expect that these solutions do not have any negative mode as in the instanton solution.Comment: Some typos are corrected and references are added with respect to the published version. 17pages, 11fi

AKARI observation of early-type galaxies in Abell 2218

We describe the AKARI InfraRed Camera (IRC) imaging observation of early-type galaxies (ETGs) in A2218 at z ≅ 0.175. With the imaging capability at 11 and 15 μm, we investigate mid-infrared (MIR) properties of ETGs in the cluster environment. Among our flux-limited sample of 22 optical red sequence ETGs, we find that more than 50% have MIR-excess emission, and the most likely cause of the MIR excess is the circumstellar dust emission from asymptotic giant branch (AGB) stars. The MIR-excess galaxies reveal a wide spread in N3-S11 (3 and 11 μm) colors, indicative of a significant spread (2–11 Gyr) in the mean ages of stellar populations. They are also preferentially located in the outer region, suggesting the environment dependence of MIR-excess ETGs over an area out to a half virial radius

Evidence for an incommensurate magnetic resonance in La(2-x)Sr(x)CuO(4)

We study the effect of a magnetic field (applied along the c-axis) on the low-energy, incommensurate magnetic fluctuations in superconducting La(1.82)Sr(0.18)CuO(4). The incommensurate peaks at 9 meV, which in zero-field were previously shown to sharpen in q on cooling below T_c [T. E. Mason et al., Phys. Rev. Lett. 77, 1604 (1996)], are found to broaden in q when a field of 10 T is applied. The applied field also causes scattered intensity to shift into the spin gap. We point out that the response at 9 meV, though occurring at incommensurate wave vectors, is comparable to the commensurate magnetic resonance observed at higher energies in other cuprate superconductors.Comment: 8 pages, including 4 figure