Abstract

In frequency domain analysis of multivariate time series, Partial Coherence (PC) is one of the important quantities. It is used in many application areas such as seismology, meteorology, neuroscience etc. It is the frequency domain analogue of partial correlation. It is derived from spectral or precision matrices, which are poorly conditioned if the complex degrees of freedom slightly exceed the dimension of the multivariate time series. Previously, shrinkage estimators have been proposed using quadratic loss function and Hilbert-Schmidt loss function. However, it is observed through simulations that some estimated PCs are high when the actual PC value equals zero, with shrinkage estimation under quadratic loss. To resolve this issue, we propose shrinkage estimators of spectral / precision matrices under Absolute loss and Huber loss. In this paper, the performance of each method is studied and evaluated extensively using simulations. The performance is measured based on the percentage relative improvement in the squared error of the proposed estimator compared to the raw estimator of Partial Coherence.