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Laplace distribution

= 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 $\widehat\sigma=S(\widehat\beta)/n$.


Laplace regression

codex/least-absolute-deviations

Laplace regression

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Laplace regression

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