1,241 research outputs found
Biased-estimations of the Variance and Skewness
Nonlinear combinations of direct observables are often used to estimate
quantities of theoretical interest. Without sufficient caution, this could lead
to biased estimations. An example of great interest is the skewness of
the galaxy distribution, defined as the ratio of the third moment \xibar_3
and the variance squared \xibar_2^2. Suppose one is given unbiased estimators
for \xibar_3 and \xibar_2^2 respectively, taking a ratio of the two does
not necessarily result in an unbiased estimator of . Exactly such an
estimation-bias affects most existing measurements of . Furthermore,
common estimators for \xibar_3 and \xibar_2 suffer also from this kind of
estimation-bias themselves: for \xibar_2, it is equivalent to what is
commonly known as the integral constraint. We present a unifying treatment
allowing all these estimation-biases to be calculated analytically. They are in
general negative, and decrease in significance as the survey volume increases,
for a given smoothing scale. We present a re-analysis of some existing
measurements of the variance and skewness and show that most of the well-known
systematic discrepancies between surveys with similar selection criteria, but
different sizes, can be attributed to the volume-dependent estimation-biases.
This affects the inference of the galaxy-bias(es) from these surveys. Our
methodology can be adapted to measurements of analogous quantities in quasar
spectra and weak-lensing maps. We suggest methods to reduce the above
estimation-biases, and point out other examples in LSS studies which might
suffer from the same type of a nonlinear-estimation-bias.Comment: 28 pages of text, 9 ps figures, submitted to Ap
Limits on the evolution of galaxies from the statistics of gravitational lenses
We use gravitational lenses from the Cosmic Lens All-Sky Survey (CLASS) to
constrain the evolution of galaxies since redshift in the current
\LCDM cosmology. This constraint is unique as it is based on a mass-selected
lens sample of galaxies. Our method of statistical analysis is the same as in
Chae (2003). We parametrise the early-type number density evolution in the form
of and the velocity dispersion as . We find that
() if we assume , implying
that the number density of early-type galaxies is within 50% to 164% of the
present-day value at redshift . Allowing the velocity dispersion to
evolve, we find that (), indicating that
the velocity dispersion must be within 57% and 107% of the present-day value at
. These results are consistent with the early formation and passive
evolution of early-type galaxies. More stringent limits from lensing can be
obtained from future large lens surveys and by using very high-redshift quasars
(z \ga 5) such as those found from the Sloan Digital Sky Survey.Comment: 10 pages (preprint format), 2 figures, ApJL in press (December 20th
issue
The Angular Power Spectrum of EDSGC Galaxies
We determine the angular power spectrum, C_l, of the Edinburgh/Durham
Southern Galaxy Catalog (EDSGC) and use this statistic to constrain
cosmological parameters. Our methods for determining C_l, and the parameters
that affect it are based on those developed for the analysis of cosmic
microwave background maps. We expect them to be useful for future surveys.
Assuming flat cold dark matter models with a cosmological constant (constrained
by COBE/DMR and local cluster abundances), and a scale--independent bias, b, we
find good fits to the EDSGC angular power spectrum with 1.11 < b < 2.35 and 0.2
< Omega_m < 0.55 at 95% confidence. These results are not significantly
affected by the ``integral constraint'' or extinction by interstellar dust, but
may be by our assumption of Gaussianity.Comment: 11 pages, 9 figures, version to appear in Ap
Large Scale Fluctuations in the X-Ray Background
We present an attempt to measure the large angular scale fluctuations in the
X-Ray Background (XRB) from the HEAO1-A2 data, expressed in terms of spherical
harmonics. We model the harmonic coefficients assuming a power spectrum and an
epoch-dependent bias parameter, and using a phenomenological scenario
describing the evolution of the X-ray sources. From the few low-order
multipoles detected above shot noise, we estimate the power-spectrum
normalization on scales intermediate between those explored by local galaxy
redshift surveys (~ 100 Mpc) and by the COBE Microwave Background measurements
(~ 1000 Mpc). We find that the HEAO1 harmonics are consistent with present
epoch rms fluctuations of the X-ray sources bx(0)sigma8 ~ 1-2 in 8 Mpc spheres.
Therefore the observed fluctuations in the XRB are roughly as expected from
interpolating between the local galaxy surveys and the COBE CMB experiment. We
predict that an X-ray all-sky surface brightness survey resolving sources a
factor of 10 fainter than HEAO1, may reveal fluctuations to significantly
larger angular scales and therefore more strongly constrain the large scale
structure of the Universe on scales of hundreds of Mpcs.Comment: 14 pages, 3 Postscript figures, uses aaspp4.sty and psfig. Revised
following referee's report. Accepted for publication in Ap
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