Point estimation for multi-spectral distributed random matrices

In this communication, we consider a p×n random matrix which is normally distributed with mean matrix M and covariance matrix Σ, where the multivariate observation xi=yi+ϵi with p dimensions on an object consists of two components, the signal yi with mean vector μ and covariance matrix Σs and noise with mean vector zero and covariance matrix Σϵ, then the covariance matrix of xi and xj is given by Σ=Cov(xi,xj)=Γ⊗(B|i-j|Σs+C|i-j|Σϵ), where Γ is a correlation matrix; B|i-j| and C|i-j| are diagonal constant matrices. The statistical objective is to consider the maximum likelihood estimate of the mean matrix M and various components of the covariance matrix Σ as well as their statistical properties, that is the point estimates of Σs,Σϵ and Γ. More importantly, some properties of these estimators are investigated in slightly more general models.