Non-linear shrinkage estimation of large-scale structure covariance

Abstract

In many astrophysical settings covariance matrices of large datasets have to be determined empirically from a finite number of mock realisations. The resulting noise degrades inference and precludes it completely if there are fewer realisations than data points. This work applies a recently proposed non-linear shrinkage estimator of covariance to a realistic example from large-scale structure cosmology. After optimising its performance for the usage in likelihood expressions, the shrinkage estimator yields subdominant bias and variance comparable to that of the standard estimator with a factor $\sim 50$ less realisations. This is achieved without any prior information on the properties of the data or the structure of the covariance matrix, at negligible computational cost.

5 pages, 5 figures; accepted for publication in MNRAS

References in corpus (3)

• Why your model parameter confidences might be too optimistic -- unbiased estimation of the inverse covariance matrix
• Nonlinear shrinkage estimation of large-dimensional covariance matrices
• Shrinkage Estimation of the Power Spectrum Covariance Matrix

Cited by in corpus (4)

• Massive data compression for parameter-dependent covariance matrices
• A First Detection of the Connected 4-Point Correlation Function of Galaxies Using the BOSS CMASS Sample
• A Test for Cosmological Parity Violation Using the 3D Distribution of Galaxies
• Residual Smoothing: Using Mocks to Correct Model Covariance Matrices