[R] IWLS vs direct ML estimation

[sandsky]

Mike,

Thank you for your valuable reply. I have read Charnes et al. (1976) and
Bradley (1973).  However, they just showed the equivalence of IWLS and ML
solutions, but didn't mentioned the advantage (or disadvantage) of IWLS
comparing with ML estimation.

Charnes, A., Frome, E. L., and Yu, P. L., 1973, The equivalence of
generalized least squares and maximum likelihood estimates in the
exponential family, J. Am. Stat. Assn., 71, 169-171. 

I think that IWLS provides the computational flexibility. Because when there
exists no analytical solution, IWLS makes it possible to solve via the
numerical solution.

Do you have any idea for this? 

Thank you,


Jinsuk Lee
Research Associate
Dept. of Industrial Engineering,
Arizona State University, USA
office: (480)-965-8468
jinsuk.lee at asu.edu


Mike Prager wrote:
> 
> 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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