First question: by invariance of MLEs, yes. However, it seems like your likelihood function is overparameterized (i.e. the likelihood is really only a function of two distinct parameters) and the MLEs you find will not be unique.
Why can't you express the likelihood with only lambda1 and lambda2 and find the MLEs numerically? [EMAIL PROTECTED] (driver_writer) wrote in message news:<[EMAIL PROTECTED]>... > If I had three parameters: eta, lambda1, lambda2 > s.t. eta = (lambda1 - lambda2), > then is it true that the MLE(eta) = MLE(lambda1) - MLE(lambda2)? > > Here the MLE (Maximum Likelihood Estimate) is derived from > d(lambda1|y)/d(lambda1) = 0. > Also, assume an average sample size (not too small, not too large). > > The reason I am asking this is because it is a little difficult to > manipulate the likelihood expression which is terms of lambda1 and > lambda2 to be an expression of eta. > > Any help would be greatly appreciated. > > -dw . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
