In MILES-PCA by Bro, Sidridopoulos and Smilde there is a possibility to model covariance between residuals in a ML fashion.
R. Bro, N. D. Sidiropoulos & A. K. Smilde, Maximum likelihood fitting using ordinary least squares algorithms, J. Chemom., 16, 387-400, 2002 Basically the homoscedasticity and independence of errors assumption can be discarded. However what you have to remember is that in ML estimation ESTIMATES of the errors/covariances/etc. are used and the qualtity of the result is also dependent on the quality of the estimates. greets, Jeroen Jansen ----- Original Message ----- From: "David Jones" <[EMAIL PROTECTED]> Newsgroups: sci.stat.edu Sent: Thursday, June 26, 2003 6:55 PM Subject: Re: Q; general statistical assumption in ML estimation > Glen wrote: > > "David Jones" <[EMAIL PROTECTED]> wrote in message > > news:<[EMAIL PROTECTED]>... > >> praxis 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? > >>> > >>> Thanks in advance. > >>> > >>> praxis > >> > >> No, or perhaps yes. > >> > >> If you are unable to "meet all the assumptions like normal > >> distribution assumption, linearity assumption, and/or > >> homoscadesticity assumption", then you need to be able to write > down > >> a model which reflects the assumptions you are prepared to make, > and > >> to be able to parameterise this model using few enough parameters > >> that > >> ML estimation will be able to produce sensible estimates. You > should > >> bear in mind the usual simple example cases where ML estimation > >> doesn't work (produces non-consistent estimates as the sample size > >> increases). > >> > >> BTW you forgot to mention the "independence of residuals" > assumption. > > > > I think you mean independence of something else, possibly errors, > > since the residuals are not independent (for starters, at least for > > normal theory regression, they add to zero). > > > > Glen > > No, I meant residuals, as opposed to fitted residuals (which may be > what you mean by "residuals"). > > David Jones > > . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
