Joachimi, B; (2017) Non-linear shrinkage estimation of large-scale structure covariance. Monthly Notices of the Royal Astronomical Society: Letters , 466 (1) L83-L87. 10.1093/mnrasl/slw240.

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Abstract

In many astrophysical settings, covariance matrices of large data sets have to be determined empirically from a finite number of mock realizations. The resulting noise degrades inference and precludes it completely if there are fewer realizations 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 optimizing 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 of ∼50 less realizations. This is achieved without any prior information on the properties of the data or the structure of the covariance matrix, at a negligible computational cost.

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