37,506 research outputs found
Estimation for almost periodic processes
Processes with almost periodic covariance functions have spectral mass on
lines parallel to the diagonal in the two-dimensional spectral plane. Methods
have been given for estimation of spectral mass on the lines of spectral
concentration if the locations of the lines are known. Here methods for
estimating the intercepts of the lines of spectral concentration in the
Gaussian case are given under appropriate conditions. The methods determine
rates of convergence sufficiently fast as the sample size so that
the spectral estimation on the estimated lines can then proceed effectively.
This task involves bounding the maximum of an interesting class of non-Gaussian
possibly nonstationary processes.Comment: Published at http://dx.doi.org/10.1214/009053606000000218 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Weak Lensing Reconstruction and Power Spectrum Estimation: Minimum Variance Methods
Large-scale structure distorts the images of background galaxies, which
allows one to measure directly the projected distribution of dark matter in the
universe and determine its power spectrum. Here we address the question of how
to extract this information from the observations. We derive minimum variance
estimators for projected density reconstruction and its power spectrum and
apply them to simulated data sets, showing that they give a good agreement with
the theoretical minimum variance expectations. The same estimator can also be
applied to the cluster reconstruction, where it remains a useful reconstruction
technique, although it is no longer optimal for every application. The method
can be generalized to include nonlinear cluster reconstruction and photometric
information on redshifts of background galaxies in the analysis. We also
address the question of how to obtain directly the 3-d power spectrum from the
weak lensing data. We derive a minimum variance quadratic estimator, which
maximizes the likelihood function for the 3-d power spectrum and can be
computed either from the measurements directly or from the 2-d power spectrum.
The estimator correctly propagates the errors and provides a full correlation
matrix of the estimates. It can be generalized to the case where redshift
distribution depends on the galaxy photometric properties, which allows one to
measure both the 3-d power spectrum and its time evolution.Comment: revised version, 36 pages, AAS LateX, submitted to Ap
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