Greetings, In the textbook treatments of WLS or GLS it is typically assumed that the error covariance is known. In some discussions it is remarked that estimates of the error covariance can also be used. This is certainly the case in my scenario -- the error covariance is experimentally estimated. However, I'm struggling a bit at the moment, because it seems to me that the presented variance expressions for the coefficients in WLS/GLS don't reflect the uncertainty associated with estimating the error covariance. For example,
y = Xb + e var(bhat) = MSE*inv(X'*W*X) where W = inv(cov(e)) It seems to me that if W is weakly estimated, the resulting intervals on bhat must be very wide, regardless of the experimental design. Does anyone have any "2-cents", or references to a treatment of this topic? Thanks in advance, C. . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
