A shrinkage linear minimum mean square error estimator

Abstract

The conventional linear minimum mean square error (LMMSE) estimator is commonly implemented through the sample covariance matrix. This estimator can only be implemented if the sample size N is higher than the observation dimension M. Moreover, this estimator performs poorly when the sample size is not sufficiently large. To address this problem, we propose a new shrinkage LMMSE estimator. The proposed estimator performs efficiently over a wide range of observation dimensions and sample sizes. In contrast to existing methods, the proposed estimator can be applied if M\geq N. Even if M