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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 > * > * For searches and help try: > * http://www.stata.com/help.cgi?search > * http://www.stata.com/support/faqs/resources/statalist-faq/ > * http://www.ats.ucla.edu/stat/stata/ -- 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 * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/faqs/resources/statalist-faq/ * http://www.ats.ucla.edu/stat/stata/ * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/faqs/resources/statalist-faq/ * http://www.ats.ucla.edu/stat/stata/

**References**:**st: A math question***From:*CJ Lan <CJ@jupiter.fl.us>

**st: RE: A math question***From:*"Feiveson, Alan H. (JSC-SK311)" <alan.h.feiveson@nasa.gov>

**st: RE: RE: A math question***From:*CJ Lan <CJ@jupiter.fl.us>

**Re: st: RE: RE: A math question***From:*David Hoaglin <dchoaglin@gmail.com>

**RE: st: RE: RE: A math question***From:*CJ Lan <CJ@jupiter.fl.us>

**RE: st: RE: RE: A math question***From:*"Feiveson, Alan H. (JSC-SK311)" <alan.h.feiveson@nasa.gov>

**Re: st: RE: RE: A math question***From:*"JVerkuilen (Gmail)" <jvverkuilen@gmail.com>

**Re: st: RE: RE: A math question***From:*Yuval Arbel <yuval.arbel@gmail.com>

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