In article <[EMAIL PROTECTED]>, driver_writer <[EMAIL PROTECTED]> wrote: >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)?
Always. The MLE maximizes the likelihood over all parameters simultaneously. >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). Only if the differentiability is there. For example, for the location parameter of a double exponential, this is not so. And if the density is of the form C*exp(|x - theta|^alpha), where alpha < 1, all order statistics are relative maxima. Yet the MLE is consistent, and is regular for alpha > .5. If alpha < .5, the asymptotic theory is highly non-regular. >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. Don't bother. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Deptartment of Statistics, Purdue University [EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558 . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
