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Minimize parameter for Least Absolute Deviation LAD

  1. Jun 9, 2010 #1
    How to compute [tex]\beta = arg min_\beta \sum_{i=1}^N {|y_i - x_i^T \beta|[/tex]
     
  2. jcsd
  3. Jun 9, 2010 #2

    statdad

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    There is no closed-form solution for this (contrary to the situation with least squares). The software you use (R, SAS, etc) use a variety of methods. check the relevant documentation for those programs.
     
  4. Jun 9, 2010 #3
    I was just interested in the calculation not in applying it to real data.
    The estimate is the median of the data x1,...,xn and I wanted to see how they derived that result.
     
  5. Jun 9, 2010 #4

    statdad

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    No, the estimates are not the medians of the x values - if that were the case we would have a "closed form" method of calculation.

    Where you may be confused is this: if you want to minimize

    [tex]
    \sum_{i=1}^n |x_i - a|
    [/tex]

    as a function of [itex] a [/itex], the solution is the sample median. This does not generalize to regression.
     
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