Regularized Tapered Sample Covariance Matrix

Covariance matrix tapers have a long history in signal processing and related fields. Examples of applications include autoregressive models (promoting banded structure) or beamforming (widening the spectral null width associated with an interferer). In this paper, focus is on high-dimensional setting where dimension $p$ high, while data aspect ratio notation="LaTeX">$n/p$ low. We propose estimator called Tabasco (TApered BAnded Shrinkage COvariance matrix) that shrinks tapered sample covariance towards scaled identity matrix. derive optimal estimated (data adaptive) regularization parameters are designed to minimize mean squared error (MSE) between proposed shrinkage true These derived under general assumption sampled from unspecified elliptically symmetric distribution finite 4th order moments (both real- complex-valued cases addressed). Simulation studies show outperforms all competing tapering estimators diverse setups. An application space-time adaptive (STAP) also illustrates benefit practical setup.