Minimize parameter for Least Absolute Deviation LAD

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  • #1
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Main Question or Discussion Point

How to compute [tex]\beta = arg min_\beta \sum_{i=1}^N {|y_i - x_i^T \beta|[/tex]
 

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  • #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.
 
  • #3
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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.
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.
 
  • #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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