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  1. Path: sparky!uunet!ogicse!usenet.coe.montana.edu!uakari.primate.wisc.edu!sdd.hp.com!news.cs.indiana.edu!umn.edu!thompson
  2. From: thompson@atlas.socsci.umn.edu (T. Scott Thompson)
  3. Newsgroups: sci.math.stat
  4. Subject: Re: Simple Proof that c=median minimizes E[ |X-c| ] needed.
  5. Message-ID: <thompson.715622525@daphne.socsci.umn.edu>
  6. Date: 4 Sep 92 16:02:05 GMT
  7. Article-I.D.: daphne.thompson.715622525
  8. References: <3SEP199213440863@utkvx2.utk.edu> <1992Sep3.221035.17952@massey.ac.nz> <thompson.715572071@daphne.socsci.umn.edu>
  9. Sender: news@news2.cis.umn.edu (Usenet News Administration)
  10. Reply-To: thompson@atlas.socsci.umn.edu
  11. Organization: Economics Department, University of Minnesota
  12. Lines: 13
  13. Nntp-Posting-Host: daphne.socsci.umn.edu
  14.  
  15. The original poster might also be interested in the fact that
  16. c = median also solves the problem
  17.  
  18.              min  E( |x-c| - |x| )
  19.               c
  20.  
  21. The advantage of this characterization over the original one is that
  22. since |x-c| - |x| is a bounded function of x, the expectation 
  23. E( |x-c| - |x| ) always exists, while E( |x-c| ) might be infinite.
  24. --
  25. T. Scott Thompson              email:  thompson@atlas.socsci.umn.edu
  26. Department of Economics        phone:  (612) 625-0119
  27. University of Minnesota        fax:    (612) 624-0209
  28.