Re: Simple Proof that c=median minimizes E[ |X-c| ] needed.

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Article #282

#282

From: T. Scott Thompson
Date: Fri, 04 Sep 1992 16:02

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The original poster might also be interested in the fact that
c = median also solves the problem

             min  E( |x-c| - |x| )
              c

The advantage of this characterization over the original one is that
since |x-c| - |x| is a bounded function of x, the expectation 
E( |x-c| - |x| ) always exists, while E( |x-c| ) might be infinite.
--
T. Scott Thompson              email:  thompson@atlas.socsci.umn.edu
Department of Economics        phone:  (612) 625-0119
University of Minnesota        fax:    (612) 624-0209

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From: thompson@atlas.socsci.umn.edu (T. Scott Thompson)
Newsgroups: sci.math.stat
Subject: Re: Simple Proof that c=median minimizes E[ |X-c| ] needed.
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Date: 4 Sep 92 16:02:05 GMT
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