Point estimation for multi-spectral distributed random matrices

✍ Scribed by Dong Q. Wang; S.E. Ahmed

• Publisher: Elsevier Science
• Year: 2009
• Tongue: English
• Weight: 142 KB
• Volume: 430
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/j.laa.2008.06.034

✦ Synopsis

In this communication, we consider a p × n random matrix X = x 1 x 2 • • • x n which is normally distributed with mean matrix M and covariance matrix , where the multivariate observation x i = y i + i with p dimensions on an object consists of two components, the signal y i with mean vector and covariance matrix s and noise i (i = 1, 2, . . . , n) with mean vector zero and covariance matrix , then the covariance matrix of x i and x j is given by = Cov(x i ,

, where 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 as well as their statistical properties, that is the point estimates of s , and . More importantly, some properties of these estimators are investigated in slightly more general models.