Double shrinkage correction in sample LMMSE estimation

Abstract

The sample linear minimum mean square error (LMMSE) es- timator undergoes high performance degradation in the small sample size regime. Herein a double shrinkage correction is proposed to alleviate this problem. First, an af ne transfor- mation of the sample covariance matrix (SCM) is considered within the LMMSE. Second, a linear transformation of that modi ed lter is proposed. The linear transformation mini- mizes the asymptotic MSE of the lter given a shrinkage of the SCM. And the shrinkage of the SCM optimizes the as- ymptotic MSE of the data covariance. Simulations highlight that the proposed estimator outperforms robust methods to the small sample size, namely LMMSE based on diagonal load- ing (DL) or Ledoit-Wolf (LW) regularizations of the SCM