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arXiv · 1411.7334

Random Matrix Derived Shrinkage of Spectral Precision Matrices

A. T. Walden·D. Schneider-Luftman
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Abstract

Much research has been carried out on shrinkage methods for real-valued covariance matrices. In spectral analysis of $p$-vector-valued time series there is often a need for good shrinkage methods too, most notably when the complex-valued spectral matrix is singular. The equivalent of the Ledoit-Wolf (LW) covariance matrix estimator for spectral matrices can be improved on using a Rao-Blackwell estimator, and using random matrix theory we derive its form. Such estimators can be used to better estimate inverse spectral (precision) matrices too, and a random matrix method has previously been proposed and implemented via extensive simulations. We describe the method, but carry out computations entirely analytically, and suggest a way of selecting an important parameter using a predictive risk approach. We show that both the Rao-Blackwell estimator and the random matrix estimator of the precision matrix can substantially outperform the inverse of the LW estimator in a time series setting. Our new methodology is applied to EEG-derived time series data where it is seen to work well and deliver substantial improvements for precision matrix estimation.

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A. T. Walden, D. Schneider-Luftman. 2014-11-26. Random Matrix Derived Shrinkage of Spectral Precision Matrices. https://doi.org/10.1109/tsp.2015.2443726

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