In article <[EMAIL PROTECTED]>, Robert J. MacG. Dawson <[EMAIL PROTECTED]> wrote: >Philip Good wrote:
>>Alas, the desirable properties of an estimate arise for an MLE only if >>that distribution is normal. > Now, why would you say that? Until you say what "the" desirable >properties of an estimate are I certainly can't confute your claim, but >I am rather confident that if you *do* I can either find a >counterexample or reassure myself that you desire some rather odd things >from estimates that I needn't trouble myself about. > So let's see your desiderata and we'll get this cleared up. "Maximum likelihood" estimators often have many of the same important properties even if the distribution assumptions may not be met, if the structural assumptions are met. For example, least squares estimators are good if the "errors" are uncorrelated with the predictor variables and with each other, and have the same variance. The lack of correlation with the predictor variables is essential, but if the other assumptions are moderately amiss, the estimators are not going to be too bad. Least squares is maximum likelihood assuming normality, and normality never happens in nature. But it usually does not matter, or does not matter much when it does. BTW, it is then "errors" for which normality is assumed, not the data. -- 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, Department 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/ . =================================================================
