Shrinkage Estimation of the Power Spectrum Covariance Matrix

Details Shrinkage Estimation of the Power Spectrum Covariance Matrix Shrinkage Estimation of the Power Spectrum Covariance Matrix

2007-11-16

arxiv.org/abs/0711.2509v2

Astronomy and Astrophysics

Astrophysics

9 pages, 7 figures (1 new), MNRAS, accepted. Changes to match accepted version, including an additional explanatory section wi

Scientific paper

10.1111/j.1365-2966.2008.13561.x

We seek to improve estimates of the power spectrum covariance matrix from a limited number of simulations by employing a novel statistical technique known as shrinkage estimation. The shrinkage technique optimally combines an empirical estimate of the covariance with a model (the target) to minimize the total mean squared error compared to the true underlying covariance. We test this technique on N-body simulations and evaluate its performance by estimating cosmological parameters. Using a simple diagonal target, we show that the shrinkage estimator significantly outperforms both the empirical covariance and the target individually when using a small number of simulations. We find that reducing noise in the covariance estimate is essential for properly estimating the values of cosmological parameters as well as their confidence intervals. We extend our method to the jackknife covariance estimator and again find significant improvement, though simulations give better results. Even for thousands of simulations we still find evidence that our method improves estimation of the covariance matrix. Because our method is simple, requires negligible additional numerical effort, and produces superior results, we always advocate shrinkage estimation for the covariance of the power spectrum and other large-scale structure measurements when purely theoretical modeling of the covariance is insufficient.

Affiliated with

Also associated with

No associations

Rating

Shrinkage Estimation of the Power Spectrum Covariance Matrix does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Shrinkage Estimation of the Power Spectrum Covariance Matrix, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Shrinkage Estimation of the Power Spectrum Covariance Matrix will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-60646