Reference for doing linear regression with mean absolute deviation?

Question

I am looking for a resource that goes over how to derive the coefficients for a linear regression model while minimizing the mean absolute deviation. I am hoping for both a mathematical and computational solution - if possible. If not, just a numerical solution would work. Can we still use gradient descent? If not, what would we use? Basically, once we set up the cost function, how do we minimize it? I'm stuck here.

Perhaps this can get you started? https://en.wikipedia.org/wiki/Quantile_regression — Tim Mak, Mar 20 '20 at 04:20

score 3 · Accepted Answer · edited Apr 19 '21 at 15:30

3

Phillips, R.F. (2002). Least absolute deviations estimation via the EM algorithm. Statistics and Computing. 12: 281-285

Dielman, T (2005). Least absolute value regression: recent contributions. Journal of Statistical Computation and Simulation. 75: 263-286

Roger Koenker has done brilliant work on 'quantile regression', I don't know whether any that might be useful?

edited Apr 19 '21 at 15:30

Alexis

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answered Mar 20 '20 at 16:33

Paul Hewson

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Reference for doing linear regression with mean absolute deviation?

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