4,301 research outputs found
Reversing the Stein Effect
The Reverse Stein Effect is identified and illustrated: A statistician who
shrinks his/her data toward a point chosen without reliable knowledge about the
underlying value of the parameter to be estimated but based instead upon the
observed data will not be protected by the minimax property of shrinkage
estimators such as that of James and Stein, but instead will likely incur a
greater error than if shrinkage were not used.Comment: Published in at http://dx.doi.org/10.1214/09-STS278 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Month-Timescale Optical Variability in the M87 Jet
A previously inconspicuous knot in the M87 jet has undergone a dramatic
outburst and now exceeds the nucleus in optical and X-ray luminosity.
Monitoring of M87 with the Hubble Space Telescope and Chandra X-ray Observatory
during 2002-2003, has found month-timescale optical variability in both the
nucleus and HST-1, a knot in the jet 0.82'' from the nucleus. We discuss the
behavior of the variability timescales as well as spectral energy distribution
of both components. In the nucleus, we see nearly energy-independent
variability behavior. Knot HST-1, however, displays weak energy dependence in
both X-ray and optical bands, but with nearly comparable rise/decay timescales
at 220 nm and 0.5 keV. The flaring region of HST-1 appears stationary over
eight months of monitoring. We consider various emission models to explain the
variability of both components. The flares we see are similar to those seen in
blazars, albeit on longer timescales, and so could, if viewed at smaller
angles, explain the extreme variability properties of those objects.Comment: 4 pages, 3 figures, ApJ Lett., in pres
Discovery of a very X-ray luminous galaxy cluster at z=0.89 in the WARPS survey
We report the discovery of the galaxy cluster ClJ1226.9+3332 in the Wide
Angle ROSAT Pointed Survey (WARPS). At z=0.888 and L_X=1.1e45 erg/s (0.5-2.0
keV, h_0=0.5) ClJ1226.9+3332 is the most distant X-ray luminous cluster
currently known. The mere existence of this system represents a huge problem
for Omega_0=1 world models.
At the modest (off-axis) resolution of the ROSAT PSPC observation in which
the system was detected, ClJ1226.9+3332 appears relaxed; an off-axis HRI
observation confirms this impression and rules out significant contamination
from point sources. However, in moderately deep optical images (R and I band)
the cluster exhibits signs of substructure in its apparent galaxy distribution.
A first crude estimate of the velocity dispersion of the cluster galaxies based
on six redshifts yields a high value of 1650 km/s, indicative of a very massive
cluster and/or the presence of substructure along the line of sight. While a
more accurate assessment of the dynamical state of this system requires much
better data at both optical and X-ray wavelengths, the high mass of the cluster
has already been unambiguously confirmed by a very strong detection of the
Sunyaev-Zel'dovich effect in its direction (Joy et al. 2001).
Using ClJ1226.9+3332 and ClJ0152.7-1357 (z=0.835), the second-most distant
X-ray luminous cluster currently known and also a WARPS discovery, we obtain a
first estimate of the cluster X-ray luminosity function at 0.8<z<1.4 and
L_X>5e44 erg/s. Using the best currently available data, we find the comoving
space density of very distant, massive clusters to be in excellent agreement
with the value measured locally (z<0.3), and conclude that negative evolution
is not required at these luminosities out to z~1. (truncated)Comment: accepted for publication in ApJ Letters, 6 pages, 2 figures, uses
emulateapj.st
Squaring the Circle and Cubing the Sphere: Circular and Spherical Copulas
Do there exist circular and spherical copulas in ? That is, do there
exist circularly symmetric distributions on the unit disk in and
spherically symmetric distributions on the unit ball in , , whose
one-dimensional marginal distributions are uniform? The answer is yes for
and 3, where the circular and spherical copulas are unique and can be
determined explicitly, but no for . A one-parameter family of elliptical
bivariate copulas is obtained from the unique circular copula in by
oblique coordinate transformations. Copulas obtained by a non-linear
transformation of a uniform distribution on the unit ball in are also
described, and determined explicitly for .Comment: 32 pages; 15 figures submitted to: Symmetr
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