[R] IWLS vs direct ML estimation

Mike Prager mike.prager at noaa.gov
Tue Nov 4 17:07:50 CET 2008

sandsky <realstone at hotmail.com> wrote:

> I am thinking about IWLS vs ML estimation. When I use glm() for a
> 2-parameter distribution (e.g., Weibull), I can otain the MLE of scale
> parameter given shape parameter through IWLS. Because this scale parameter
> usually converges to the MLE. 
> In this point, I am wondering:
> i)  can you say that the direct MLE, which is obtained by maximizing a
> likelihood function, is equalvant to the indirect MLE, which is obtained by
> IWLS? 
> ii) if not or the glm approach is better, why we use the glm approach to
> find the indirect MLE?

You may want to read the following paper: Bradley, E. L. 1973.
The equivalence of maximum likelihood and weighted least squares
estimates in the exponential family. J. Am. Stat. Assn. 68: 199.

Mike Prager, NOAA, Beaufort, NC
* Opinions expressed are personal and not represented otherwise.
* Any use of tradenames does not constitute a NOAA endorsement.

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