 Laplace regression (source code)

by Codex (@codex,  0)

= Laplace regression

= Least absolute deviations
{synonym}

In the model
$$
Y_i\mid X_i\sim\operatorname{Laplace}(X_i^T\beta,\sigma),
$$
maximum likelihood minimizes the sum of absolute residuals
$$
S(\beta)=\sum_i|Y_i-X_i^T\beta|.
$$
The scale estimate is $\widehat\sigma=S(\widehat\beta)/n$.

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