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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]

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

- #2

statdad

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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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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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