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RE: st: RE: RE: A math question


From   "Feiveson, Alan H. (JSC-SK311)" <alan.h.feiveson@nasa.gov>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   RE: st: RE: RE: A math question
Date   Fri, 21 Dec 2012 12:25:02 -0600

Sort of. A more precise way to state your point might be that the sum of absolute values of the errors Sum|e_i|, where e_i = actual_i - predicted_i, is minimized  when the predicted value is the median. 

Al

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Yuval Arbel
Sent: Friday, December 21, 2012 12:13 PM
To: statalist@hsphsun2.harvard.edu
Subject: Re: st: RE: RE: A math question

Regarding the linear programing you are obviously correct: the derivative is not defined mathematically at x=0. Nevertheless, the important point that rises from the discussion is that the median is the absolute value function.

On Fri, Dec 21, 2012 at 8:41 AM, JVerkuilen (Gmail) <jvverkuilen@gmail.com> wrote:
> On Fri, Dec 21, 2012 at 11:29 AM, Feiveson, Alan H. (JSC-SK311) 
> <alan.h.feiveson@nasa.gov> wrote:
>> You can't optimize a function of median |ei| by setting it's derivative to zero because the partial derivatives don't exist at ei = 0. You would have do something like linear programming (as is done in LAD regression).
>>
>
> True but you can do some nifty approximations, which is how interior 
> point/barrier methods work, by approximating the L1 distance function 
> with a sequence of functions that are smooth but grow arbitrarily 
> close to L1.
>
> http://en.wikipedia.org/wiki/Interior_point_method
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--
Dr. Yuval Arbel
School of Business
Carmel Academic Center
4 Shaar Palmer Street,
Haifa 33031, Israel
e-mail1: yuval.arbel@carmel.ac.il
e-mail2: yuval.arbel@gmail.com
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