In parameter estimation for linear mixed model for unknown variance, I met some statements saying that "we assume
G (as variance) is only known up to its variance parameter
G is represented as
I met this statement in the book Generalized, Linear, and Mixed Models.
Examples of these statements can be found in page 12 in this one.
I wonder what is the relationship between
v? To estimate
G, we need to maximize a likelihood function of
l(v) = XG(v)Y
(of course the actual likelihood is much more complicated than this simple one)
So, I wonder how we could write
G(v) as a function of
v explicitly, so that we could maximize it?
A similar question has been asked here, but I am looking for a more concrete solution, which I assume will be helpful for the ones who are interesting in implementing their own linear mixed model.