Consistent estimate of a residuals covariance for the estimation of noise covariance

The authors derived a best linear unbiased estimate (BLUE) for the estimation of the noise covariance matrix, where the covariance matrix of the residuals of the linear regression equation is required. In the previous paper, the sample covariance of the residuals was given, but the consistency of the sample covariance was not analyzed. In this paper, theoretical analysis shows that the proposed sample covariance matrix is a consistent estimate of the covariance matrix in a certain sense.