Maximum-likelihood estimation necessarily requires one more assumption than OLS - You have to specify the statistical distribution of the data.
In a multiple regression setup if you specify that the errors are normal, mean zero, independent, and equal variance, then the ML and OLS coefficient estimates are identical. If you specify some other distribution for the errors, then the ML coefficients will be something different. -Dick Startz On Wed, 25 Jun 2003 17:51:16 -0400, Rich Ulrich <[EMAIL PROTECTED]> wrote: >On Wed, 25 Jun 2003 00:15:26 -0500, "praxis" <[EMAIL PROTECTED]> >wrote: > >> Hi all. >> >> Assuming I do a multiple regression using ML estimation instead of OLS, do I >> still need to meet all the assumptions like normal distribution assumption, >> linearity assumption, and/or homoscadesticity assumption? If yes, could >> anyone explain why? > >For the same test, you need the same assumptions. >I know that you can set up Discriminant function with >other assumptions, and an improved error model, using >Logistic regression, and its ML solution. > >However, in particular, I don't remember this -- >Is there a particular ML estimation of "multiple >regression"? Is there an ML solution to the Normal >equations that isn't the OLS solution? > > >Here is one way to think about tests in general. >The OLS test, or any test, is made *efficient* when >it makes a useful, true assumption. > >Whenever we abandon a *useful* assumption -- such >as, any of those three named above -- we have to >abandon some efficiency at the same time. > >It is really a useful exercise, now and then, to figure >out how to get different results in two analyses. What >feature does X test, and what will disrupt X, and what >is X robust against? > >[Can you show what will make the correlated t-test >far less powerful than the t-test for groups? ] ---------------------- Richard Startz [EMAIL PROTECTED] Lundberg Startz Associates . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
