Least Absolute Deviations - Variations, Extensions, Specializations

Variations, Extensions, Specializations

The least absolute deviation problem may be extended to include multiple explanators, constraints and regularization, e.g., a linear model with linear constraints:

minimize

subject to, e.g.,

where is a column vector of coefficients to be estimated, b is an intercept to be estimated, x_i is a column vector of the ith observations on the various explanators, y_i is the ith observation on the dependent variable, and k is a known constant.

Regularization with LASSO may also be combined with LAD.